M4 Mag. Prop. & AC PDF - Physics Past Paper

Magnetic field ❑ A moving charge or a current creates a magnetic field in the surrounding space ❑ The magnetic field exerts a force on any other moving charge or current that is present in the field ❑ A magnet always comes with a north and a south pole. There is no experimental evidence that...

Magnetic field ❑ A moving charge or a current creates a magnetic field in the surrounding space ❑ The magnetic field exerts a force on any other moving charge or current that is present in the field ❑ A magnet always comes with a north and a south pole. There is no experimental evidence that one isolated magnetic pole exists; poles always appear in pairs. ❑ If a bar magnet is broken in two, each broken end becomes a pole ❑ Like electric field, magnetic field is a vector field—that is, a vector quantity associated with each point in space. We will use the symbol B for magnetic field. ❑ At any position the direction of magnetic field is defined as the direction in which the north pole of a compass needle tends to point 1  Magnetic force on moving charges ❑ A force on a charge q moving with velocity v in a magnetic field B is given by, ❑ The SI unit of magnetic field is Tesla (T). Another unit of B, the gauss (1 G = 10-4 T) , is also in commonly used. 2  Magnetic force on moving charges ❑ To find the direction of the magnetic filed, Draw the v vector and B vector with their tails together, as in Figure. Using the right hand, point your fingers towards velocity and curl your fingers towards magnetic field. Your thumb then points in the direction of the force for a positive charge. For a negative charge the thumb points in the opposite direction of the force. 3 Magnetic force on moving charges 4 Magnetic force on moving charges 5  Magnetic flux ❑ We define the magnetic flux through a surface just as we defined electric flux, ❑ The SI unit of magnetic flux is equal to the unit of magnetic field (1 T) times the unit of area (1 m2). This unit is called the weber. 6  Gauss’s Law for Magnetism ❑ Unlike electric charge you cannot have a single magnetic charge. Another way to say is magnetic monopole does not exist. So the flux through a closed surface is always zero. So the Gauss’s law for magnetism is , 7 Magnetic field direction of a current element ❑ The magnetic field direction will be in a plane perpendicular to the current. The direction of magnetic field is given by the right-hand rule: Curl your fingers on the right hand so that your right thumb points in the direction of current ; your fingers shows the direction of the magnetic field. 8  Ampere’s Law ❑ The closed line integral of the magnetic field equals µ0 times the algebraic sum of the currents. ❑ We can choose any arbitrary closed curve for the line integral. For doing the algebraic sum of currents, we have to use a sign rule: Curl the fingers of your right hand around the integration path so that they curl in the direction of integration. Then your right thumb indicates the positive current direction. Currents that pass in this direction are positive; those in the opposite direction are negative. 9  Ampere’s Law Find the magnetic field of a long, straight, current-carrying conductor. 10 Ampere’s Law 11 Ampere’s Law 12 Ampere’s Law 13 Ampere’s Law 14 Ampere’s Law 15 Ampere’s Law 16  The Bohr magneton ❑ What is the source of magnetic field inside materials ? The atoms that make up all matter contain moving electrons, and these electrons form microscopic current loops that produce magnetic fields of their own. In many materials these currents are randomly oriented and cause no net magnetic field. But in some materials an external field can cause these loops to become oriented preferentially with the field, so their magnetic fields add to the external field. We then say that the material is magnetized. ❑ Let’s look at how these microscopic currents come about. Figure shows a simplified model of an electron in an atom. We picture the electron as moving in a circular orbit with radius r and speed v. This moving charge is equivalent to a current loop. The orbital period T (the time for the electron to make one complete orbit) is the orbit circumference divided by the electron speed: T = 2πr/v. The equivalent current I is the total charge passing any point on the orbit per unit time, which is just the magnitude e of the electron charge divided by the orbital period T: 17  The Bohr magneton ❑ Magnetic moment gives the magnetic strength of a magnet. A current loop with area A and current I has a magnetic dipole moment µ given by µ = IA; for the orbiting electron, the area of the loop is A = πr2. The magnetic moment is then, ❑ It is useful to express µ in terms of the orbital angular momentum L of the electron. For a particle moving in a circular path, the magnitude of angular momentum equals the magnitude of momentum mv multiplied by the radius r, L = mvr. So we can write magnetic moment as, ❑ Atomic angular momentum is quantized; its component in a particular direction is always an integer multiple of h/2π. 18  The Bohr magneton ❑ If L = h/2π. Then the magnetic moment, ❑ This quantity is called the Bohr magneton, denoted by µB. Its numerical value is, ❑ Electrons also have an intrinsic angular momentum, called spin, that is not related to orbital motion but that can be pictured in a classical model as spinning on an axis. This angular momentum also has an associated magnetic moment, and its magnitude is almost exactly one Bohr magneton. 19  Magnetic materials - Paramagnetism ❑ Atoms with unpaired electrons have a net magnetic moment and when placed in an external magnetic field, the magnetic moments of atoms align with the external field. This is called paramagnetism. Paramagnetic material gets attracted to the external magnet. Example: Sodium :1s2 2s2 2p6 3S1 ❑ Because magnetic moments align in the direction of external magnetic field B0, the field inside a paramagnetic material is always more than the external field, ❑ Where M is the total magnetic moment per unit volume V in the material. It is called the magnetization of the material, ❑ Magnetic field inside a paramagnetic material is greater by a dimensionless factor called the relative permeability of the material (Km), than it would be if the material were replaced by vacuum. 20  Magnetic materials - Paramagnetism ❑ To find the magnetic field inside a paramagnetic material using Ampere's law, we can replace μ0 by Km μ0. This product is usually denoted as μ and is called the permeability of the material: ❑ The amount by which the relative permeability differs from unity is called the magnetic susceptibility,. Susceptibility is always positive for paramagnetic materials. ❑ Thermal motion reduces the alignment of magnetic moments. For this reason, paramagnetic susceptibility always decreases with increasing temperature T. And the magnetization M can be expressed as, ❑ This relationship is called Curie’s law. The quantity C is a constant, called the Curie constant. B is the external magnetic field. 21  Magnetic materials - Diamagnetism ❑ Atoms with completely paired electrons have no net magnetic moment and when placed in an external magnetic field, an induced magnetic field is created in the opposite direction (Faraday's law). This is called diamagnetism. Diamagnetic material gets repelled by the external magnet. Example: Neon: 1s2 2s2 2p6 3S1 ❑ The relative permeability (Km) of the diamagnetic material is slightly below 1, so they always have negative susceptibility (χm) 22  Magnetic materials - Ferromagnetism ❑ In ferromagnetic materials such as iron strong interactions between atomic magnetic moments cause them to line up parallel to each other in regions inside the material called magnetic domains, even when no external field is present. Figure shows an example of magnetic domain structure. Within each domain, nearly all of the atomic magnetic moments are parallel. ❑ When there is no externally applied field, the domain magnetizations are randomly oriented. But when an external field is present, the domains tend to orient themselves parallel to the field. The domain boundaries also shift; the domains that are magnetized in the field direction grow, and those that are magnetized in other directions shrink. For ferromagnets, the relative permeability Km is much larger than unity. As a result, an object made of a ferromagnetic material such as iron is strongly magnetized by the field from a permanent magnet and is attracted to the magnet. A paramagnetic material such as aluminum is also attracted to a permanent magnet, but Km for paramagnetic materials is so much smaller for such a material than for ferromagnetic materials that the attraction is very weak. Thus a magnet can pick up iron nails, but not aluminum cans. 23  Magnetic materials - Ferromagnetism ❑ As the external field is increased, a point is eventually reached at which nearly all the magnetic moments in the ferromagnetic material are aligned parallel to the external field. This condition is called saturation magnetization; after it is reached, further increase in the external field causes no increase in magnetization ❑ For many ferromagnetic materials the relationship of magnetization to external magnetic field is different when the external field is increasing from when it is decreasing. Figure shows this relationship for such a material. When the material is magnetized to saturation and then the external field is reduced to zero, some magnetization remains. This behavior is characteristic of permanent magnets, which retain most of their saturation magnetization when the magnetizing field is removed. To reduce the magnetization to zero requires a magnetic field in the reverse direction ❑ This behavior is called hysteresis, and the curve of magnetization vs Applied Magnetic field is called a hysteresis loop. Magnetizing and demagnetizing a material that has hysteresis involve the dissipation of energy, and the temperature of the material increases during such a process. 24 Magnetic materials - Ferromagnetism 25 ALTERNATING CURRENT  Kirchhoff’s Rules ❑ Kirchhoff’s rules are the following two statements: ❑ The junction rule is based on conservation of electric charge. No charge can accumulate at a junction, so the total charge entering the junction per unit time must equal the total charge leaving per unit time. Charge per unit time is current, so if we consider the currents entering a junction to be positive and those leaving to be negative, the algebraic sum of currents into a junction must be zero. ❑ The loop rule is a statement that the electrostatic force is conservative. Suppose we go around a loop, measuring potential differences across successive circuit elements as we go. When we return to the starting point, we must find that the algebraic sum of the potential differences is zero. 27  Sign conventions for the loop Rule ❑ In applying the loop rule, we need some sign conventions. Starting at any point in the circuit, we imagine traveling around a loop, adding emfs and IR terms as we come to them. When we travel through a source in the direction from - to +, the emf is considered to be positive; when we travel from + to -, the emf is considered to be negative. When we travel through a resistor in the same direction as the assumed current, the IR term is negative. When we travel through a resistor in the direction opposite to the assumed current, the IR term is positive. 28 Single loop circuit Find the Current in the circuit. 29 Single loop circuit 30  RC circuits – Charging a capacitor ❑ In the circuits we have analyzed up to this point, we have assumed that all the emfs and resistances are constant so that all the potentials and currents are also independent of time. But in charging or discharging a capacitor the currents and voltages do change with time. ❑ Figure shows a simple circuit for charging a capacitor. A circuit that has a resistor and a capacitor in series is called an R-C circuit. We idealize the battery to have a constant emf E ❑ We begin with the capacitor initially uncharged; then at some initial time t = 0, we close the switch, completing the circuit and permitting current around the loop to begin charging the capacitor 31  RC circuits – Charging a capacitor ❑ Because the capacitor is initially uncharged, the potential difference Vbc across it is zero at t = 0. At this time, from Kirchhoff’s loop law, the voltage Vab across the resistor R is equal to the battery emf E. The initial (t = 0) current through the resistor, which we will call I0 , is given by Ohm’s law: I0 = vab/R = E/R. ❑ As the capacitor charges, its voltage Vbc increases and the potential difference Vab across the resistor decreases, corresponding to a decrease in current. The sum of these two voltages is constant and equal to E. After a long time the capacitor is fully charged, the current decreases to zero, and Vab across the resistor becomes zero. Then the entire battery emf E appears across the capacitor and Vbc = E. ❑ Now let’s derive an expression for charge stored in the capacitor with time. 32  RC circuits – Charging a capacitor ❑ Let q represent the charge on the capacitor and i the current in the circuit at some time t after the switch has been closed. The instantaneous potential differences Vab and Vbc are, ❑ Using these in Kirchhoff’s loop rule, we find ❑ At time t = 0, when the switch is first closed, the capacitor is uncharged, and so q = 0. Substituting q = 0 into Equation, we find that the initial current I0 is given by I0 = E/R. 33  RC circuits – Charging a capacitor ❑ As the charge q increases, the term q/RC becomes larger and the capacitor charge approaches its final value, which we will call Qf. The current decreases and eventually becomes zero. When i = 0, Equation gives, , ❑ We can derive general expressions for charge q and current i as functions of time. i = dq/dt, so the previous equation becomes, ❑ Rearrange, ❑ Integrate on both sides. We change the integration variables to q′ and t′ so that we can use q and t for the upper limits. The lower limits are q′ = 0 and t′ = 0 ❑ ➔ 34  RC circuits – Charging a capacitor ❑ Take exponential on both sides and solving for q, we find ❑ ➔ ❑ The instantaneous current i is just the time derivative of charge, 35  RC circuits – Time constant ❑ After a time equal to RC, the current in the R-C circuit has decreased to 1/e (about 0.368) of its initial value. At this time, the capacitor charge has reached (1 – 1/e) = 0.632 of its final value Qf. The product RC is therefore a measure of how quickly the capacitor charges. We call RC the time constant or the relaxation time of the circuit, denoted by τ: ❑ When time constant is small, the capacitor charges quickly; when it is larger, the charging takes more time. If the resistance is small, it’s easier for current to flow, and the capacitor charges more quickly. 36  RC circuits – Discharging a capacitor ❑ Now suppose that after the capacitor has acquired a charge Q0 , we remove the battery from our R-C circuit and connect points a and c and at the same instant reset our stopwatch to t = 0; at that time, q = Q0. The capacitor then discharges through the resistor, and its charge eventually decreases to zero ❑ Again let i and q represent the time-varying current and charge at some instant after the connection is made. ❑ Then Kirchhoff’s loop rule gives, ➔ ❑ The current i is now negative, this is because positive charge q is leaving the left-hand capacitor plate in Figure, so the current is in the direction opposite to that shown. At time t = 0, when q = Q0 , the initial current is I0 = -Q0/RC 37  RC circuits – Discharging a capacitor ❑ To find q as a function of time, we rearrange equation, again change the variables to q′ and t′ and integrate. This time the limits for q′ are Q0 to q: 38 RC circuits – Discharging a capacitor 39  Electromagnetic Induction ❑ Michael Faraday in 1831 discovered that a coil of wire in a changing magnetic field produces current in the coil. We call this an induced current, and the corresponding emf required to cause this current is called an induced emf. 40  Faraday’s law ❑ Faraday’s law states that the induced emf in a closed loop equals the negative of the time rate of change of magnetic flux through the loop. ❑ Where , ❑ If B is uniform over a flat area A, then ❑ If a coil has N identical turns and If ɸB is the flux through each turn, the total emf in a coil with N turns is, 41 Faraday’s Law 42 Faraday’s Law 43  Direction of the induced current – Lenz’s law ❑ Lenz’s law gives the direction of the induced current. Lenz’s law states that: induced electric current flows in a direction such that the current opposes the change in magnetic field that induced it. 44 Direction of the induced current – Lenz’s law 45  Mutual induction ❑ Consider two neighboring coils of wire, as in Figure. A current flowing in coil 1 produces a magnetic field and hence a magnetic flux through coil 2. If the current in coil 1 changes, the flux through coil 2 changes as well; according to Faraday’s law, this induces an emf in coil 2. In this way, a change in the current in one circuit can induce a current in a second circuit. ❑ The emf induced in the second coil is given by, , where ɸB2 is the changing flux through the second coil. ❑ Total Flux N2 ɸB2 is proportional to current ii in the first coil. Introducing a proportionality constant M21, called the mutual inductance of the two coils, we can write, ➔ ❑ So we can write, ➔ 46  Mutual induction ❑ Consider the opposite situation where there is a changing current through the second coil which induces an emf in the first coil. It turns out that the corresponding constant M12 is always equal to M21. We call this common value simply the mutual inductance, denoted by the symbol M without subscripts. The SI unit of mutual inductance is called the henry (H). 47  Drawbacks and uses of Mutual Inductance ❑ Mutual inductance can be a nuisance in electric circuits, since variations in current in one circuit can induce unwanted emfs in other nearby circuits. To minimize these effects, multiple-circuit systems must be designed so that M is as small as possible; for example, two coils would be placed far apart. ❑ Happily, mutual inductance also has many useful applications. A transformer, used in alternating-current circuits to raise or lower voltages works using mutual induction. A time-varying alternating current in one coil of the transformer produces an alternating emf in the other coil; the value of M, which depends on the geometry of the coils, determines the amplitude of the induced emf in the second coil and hence the amplitude of the output voltage. 48  Inductance – Self Inductance ❑ A current in a circuit sets up a magnetic field that causes a magnetic flux through the same circuit; this flux changes when the current changes. Thus any circuit that carries a varying current has an emf induced in it by the variation in its own magnetic field. Such an emf is called a self-induced emf. ❑ By Lenz’s law, a self-induced emf opposes the change in the current that caused the emf and so tends to make it more difficult for variations in current to occur. So if the current is decreasing, self-induced emf will try to increase current and if the current is increasing, self-induced emf will try to decrease current ❑ we define the self-inductance L of the circuit as, ❑ Self inductance is called just inductance and the SI unit is henry. 49  Inductance – Self Inductance ❑ Rearranging the equation, NɸB = Li ❑ Differentiate with respect to time, ❑ From Faraday’s law for a coil with N turns, the self-induced emf is, ❑ Comparing equations, ❑ The minus sign is a reflection of Lenz’s law; it says that the self induced emf in a circuit opposes any change in the current in that circuit. 50  Inductors as circuit elements ❑ A circuit device that is designed to have a particular inductance is called an inductor, or a choke. The usual circuit symbol for an inductor is, ❑ Like resistors and capacitors, inductors are among the indispensable circuit elements of modern electronics. Their purpose is to oppose any variations in the current through the circuit. An inductor in a direct-current circuit helps to maintain a steady current despite any fluctuations in the applied emf; in an alternating-current circuit, an inductor tends to suppress variations of the current that are more rapid than desired. ❑ In an electrical circuit, the potential difference across the inductor is given by, 51  Current growth in an R-L circuit ❑ A circuit that includes both a resistor and an inductor is called an R-L circuit. The inductor helps to prevent rapid changes in current, which can be useful if a steady current is required but the source has a fluctuating emf. ❑ Let i be the current at some time t after switch S1 is closed, and let di/dt be its rate of change at that time. The potential differences vab (across the resistor) and vbc a b c (across the inductor) are, ❑ If the current is increasing, the inductor will behave like a resistor, trying to resist the current flow. We apply Kirchhoff’s loop rule, starting at the negative terminal and proceeding counterclockwise around the loop, 52  Current growth in an R-L circuit ❑ First, we rearrange the equation, ❑ Then we integrate both sides, renaming the integration variables i’ and t’ so that we can use i and t as the upper limits. The lower limit for each integral is zero, corresponding to zero current at the initial time t = 0. ❑ Now we take exponentials of both sides and solve for i. 53  Current growth in an R-L circuit ❑ Taking a derivative, ❑ From the equations, at time t = 0, i = 0 and di/dt = 𝛆/L. At t = ∞, i =E/R and di/dt = 0 ❑ As Figure shows, the instantaneous current i first rises rapidly, then increases more slowly and approaches the final value I = E/R. At a time equal to L/R, the current has risen to (1 – 1/e), or about 63%, of its final value. The quantity L/R is therefore a measure of how quickly the current builds toward its final value; this quantity is called the time constant for the circuit, denoted by 𝛕: 54  Current decay in an R-L circuit ❑ We want to establish a current in the R-L circuit and then remove the battery and see how the current decays in an R-L circuit ❑ Suppose switch S1 in the circuit has been closed for a while and the current has reached the value I0. To remove the battery from the circuit, open switch S1 and close the switch S2 and this is our starting time, t = 0. ❑ Let i be the current at some time t after switch S2 is closed, and let di/dt be its rate of change at that time. Using Kirchhoff's law, - Rearranging the equation, 𝑑𝑖 𝑅 = - dt 𝑖 𝐿 55  Current decay in an R-L circuit ❑ Integrate on both sides, current goes from I0 to i, 𝑖 𝑑 𝑖ƴ 𝑡 𝑅 ‫𝑖 𝐼׬‬ƴ = ‫׬‬0 − 𝐿 dt’ 0 −𝑅 ln(𝑖 − 𝐼0 ) = t 𝐿 𝑖 −𝑅 ln = t 𝐼0 𝐿 −𝑅 𝑖 𝑡 ❑ Take exponential on both sides, =𝑒 𝐿 𝐼0 As Figure shows, current doesn't instantaneously become zero even though there is no battery. Current will slowly decay to become zero. 56  L-C circuit ❑ A circuit containing an inductor and a capacitor shows an entirely new mode of behavior, characterized by oscillating current and charge ❑ When the switch is closed, the capacitor begins to discharge, producing a current in the circuit. The current, in turn, creates a magnetic field in the inductor. The net effect of this process is a transfer of energy from the capacitor, with its diminishing electric field, to the inductor, with its increasing magnetic field. When the capacitor is completely discharged, all the energy is stored in the magnetic field of the inductor. At this instant, the current is at its maximum value. After reaching its maximum, the current continues to transport charge between the capacitor plates, thereby recharging the capacitor. Since the inductor resists a change in current, current continues to flow, even though the capacitor is discharged. This continued current causes the capacitor to charge with opposite polarity. The electric field of the capacitor increases while the magnetic field of the inductor diminishes, and the overall effect is a transfer of energy from the inductor back to the capacitor. When fully charged, the capacitor once again transfers its energy to the inductor until it is again completely discharged, Then, in the last part of this cyclic process, energy flows back to the capacitor, and the initial state of the circuit is restored. 57 L-C circuit 58  Electrical oscillations in an L-C circuit ❑ We apply Kirchhoff’s loop rule to the circuit in Figure. Starting at the lower-right corner of the circuit and adding voltages as we go clockwise around the loop, we obtain ❑ Since i = dq/dt, it follows that di/dt = d2q/dt2. We substitute this expression into the above equation and divide by -L to obtain ❑ This equation has the same form as the equation for simple harmonic motion for a spring – mass system, 𝑘 ❑ Where, and angular frequency, 𝜔 =. Where the amplitude A and 𝑚 the phase angle ɸ 59  Electrical oscillations in an L-C circuit ❑ Comparing with the simple harmonic motion, the capacitor charge q is given by, ❑ And the angular frequency of oscillation is given by, ❑ The instantaneous current i = dq/dt is, ❑ Thus the charge and current in an L-C circuit oscillate sinusoidally with time, with an angular frequency determined by the values of L and C. 60 Electrical oscillations in an L-C circuit 61 Electrical oscillations in an L-C circuit 62  Alternating current ❑ AC source is any device that supplies a sinusoidally varying voltage v or current i. The usual circuit-diagram symbol for an ac source is ❑ A sinusoidal voltage might be described by a function as, ❑ In this expression, lowercase v is the instantaneous potential difference; uppercase V is the maximum potential difference, which we call the voltage amplitude; and ⍵ is the angular frequency, equal to 2π times the frequency f. ❑ In india, f = 50 Hz or ⍵ = 314 rad/s is used. ❑ Similarly, a sinusoidal current can be represented as, 63  Resistor in an ac circuit ❑ First let’s consider a resistor with resistance R through which there is a sinusoidal current given by i = I cos ⍵t. From Ohm’s law the instantaneous voltage vR across the resistor is, ❑ The maximum value of the voltage vR is VR , the voltage amplitude: ❑ Hence we can also write,. Both the current i and the voltage vR are proportional to cos ⍵t, so the current is in phase with the voltage. 64  Inductor in an ac circuit ❑ Consider an inductor with inductance L through which there is a sinusoidal current given by i = I cos ⍵t. The instantaneous voltage vL across the inductor is, ❑ Using the formula, Cos(A + 900) = - sin A, ❑ This result shows that the voltage can be viewed as a cosine function with 90 degrees ahead of the current. ❑ So the current is and voltage is ❑ we call ɸ the phase angle; it gives the phase of the voltage relative to the current. For a pure resistor, ɸ = 0, and for a pure inductor, ɸ = 90 65  Inductor in an ac circuit ❑ From the equation, the amplitude VL of the inductor voltage is, ❑ The voltage across the inductor can be written in a similar form as that of a resistor as, ❑ Where XL is called the Inductive reactance, ❑ Because XL is the ratio of a voltage and a current, its SI unit is the ohm, the same as for resistance. Since XL is proportional to frequency, a high-frequency voltage applied to the inductor gives only a small current, while a lower-frequency voltage of the same amplitude gives rise to a larger current. Inductors are used in some circuit applications to block high frequencies while permitting lower frequencies or dc to pass through. A circuit device that uses an inductor for this purpose is called a low-pass filter. 66  Cpacitor in an ac circuit ❑ Consider a capacitor with capacitance C through which there is a sinusoidal current given by i = I cos ⍵t. The current i is related to charge q on the capacitor plate by, ❑ To get charge, we can integrate the equation ‫ 𝐼 ׬ = 𝑞𝑑 ׬‬cos 𝜔𝑡 𝑑𝑡 ➔ ❑ Voltage across the capacitor, vc = q/C ➔ ❑ Using Identity, cos(A – 900) = sin A, ❑ This corresponds to a phase angle ɸ = -900. Here Voltage lags the current by 900. 67  Capacitorr in an ac circuit ❑ From the equations, the amplitude Vc of the capacitor voltage is, ❑ The voltage across the capacitor can be written in a similar form as that of a resistor as, ❑ Where Xc is called the capacitive reactance, ❑ Because Xc is the ratio of a voltage and a current, its SI unit is the ohm, the same as for resistance. The capacitive reactance of a capacitor is inversely proportional both to the capacitance C and to the angular frequency ⍵; the greater the capacitance and the higher the frequency, the smaller the capacitive reactance XC. So Capacitors tend to pass high-frequency current and to block low-frequency currents and dc, just the opposite of inductors. A device that preferentially passes signals of high frequency is called a high-pass filter. 68 Comparing ac Circuit elements - Summary 69