Electric Circuits Physics: Formulas, Definitions, and Energy

Summary Electric Circuit II Physics You can apply the gained knowledge about electrostatics on the topic of electric circuit. You can draw electric circuits using common symbol and notation. You can distinguish between voltage, current and resistance. You can apply the rules of parallel and seri...

Summary Electric Circuit II Physics You can apply the gained knowledge about electrostatics on the topic of electric circuit. You can draw electric circuits using common symbol and notation. You can distinguish between voltage, current and resistance. You can apply the rules of parallel and series circuits and calculate equivalent resistance and the corresponding currents and voltages. You can measure current and the voltage inside an electric circuit. You can calculate electrical energy and electrical power. You can distinguish between the three poles of an ordinary socket in Switzerland. You can explain the difference between AC and DC You can explain the health risk due to an electric shock. You can explain the safety measures like circuit breaker, RCD and protective earth. Electric Circuits Definition Ein Bild, das Text, Reihe, Schrift, Zahl enthält. Automatisch generierte Beschreibung  Technical current direction Electrons are moving -\> physical current direction The technical current direction is always from positive to negative. The physical current direction depends on the particle. Electric Current Definition The electric current [I ]{.math.inline}indicates the amount of charges [*ΔQ*]{.math.inline} flows through a conductor in a time interval [*Δt*]{.math.inline}: \ [\$\$I = \\frac{\\mathrm{\\Delta}Q}{\\mathrm{\\Delta}t}\$\$]{.math.display}\ The SI-unit is Ampere (A), \ [\$\$\\left\\lbrack I \\right\\rbrack = A = \\frac{C}{s}\$\$]{.math.display}\ Remark: - Only free moving charges make up the current. - The charges can be positive or negative. - In most situations, the charges are electrons that can freely move in metals. Resistance Definition If in a conductor the current is I where the applied voltage is V, its resistance R is defined by \ [\$\$R = \\frac{V}{I}\$\$]{.math.display}\ The SI-unit for electrical resistance is given by Ohm [*Ω*]{.math.inline} which is Volts per Ampere. \ [\$\$\\left\\lbrack R \\right\\rbrack = \\ \\mathrm{\\Omega} = \\frac{V}{A}\$\$]{.math.display}\ Voltage Definition The electric voltage is the electric potential difference between two points, A and B, in an electric field. \ [*V*~AB~ = *Δ*⌀ = ⌀~*B*~ − ⌀~*A*~]{.math.display}\ The work done to transfer a charge q in an electric field from A to B is given by \ [*W*~AB~ = *q* \* *V*~AB~]{.math.display}\ If the electric field is generated by a point charge, the voltage can be expressed by \ [\$\$V\_{\\text{AB}} = k\_{e}\*Q\*(\\frac{1}{r\_{B}} - \\frac{1}{r\_{A}})\$\$]{.math.display}\ And therefore, the corresponding work done to transfer a test charge from A to B is given by \ [\$\$W\_{\\text{AB}} = k\_{e}\*Q\*q\*(\\frac{1}{r\_{B}} - \\frac{1}{r\_{A}})\$\$]{.math.display}\ Ohmic Resistor Definition The following applies to an ohmic resistor: \ [\$\$R = \\frac{V}{I} = const\$\$]{.math.display}\ Parallel Circuits Definition The equivalent resistance of multiple resistors [*R*~1~, *R*~2~, ..., *R*~*n*~]{.math.inline} connected in parallel is given by: \ [\$\$\\frac{1}{R\_{\\text{eq}}} = \\frac{1}{R\_{1}} + \\frac{1}{R\_{2}} + \\ldots + \\frac{1}{R\_{n}}\$\$]{.math.display}\ \ [*R*~eq~ \ *R*~1~, *R*~2~]{.math.display}\  In a **series circuit**, the **current** remains the same throughout all components, while the **voltage** divides among them. The formula to calculate the total voltage in a circuit in series is given on the left side. Measurement Current and Voltage Definition The multimeter used as the voltmeter can measure the voltage difference between two points before and after a consumer. You therefore calculate the voltage drop between the two points which are connected. If you do not know the range in advance, start with a large range and go to smaller range step-by-step to increase accuracy.  Measurement of current using a multimeter works like the measurement of voltage. The chosen range is relevant. Again, if you do not know the relevant range, start with the large range and reduce it step-by-step to prevent any damage to the multimeter. It is therefore measured in series since the same current flows through the ammeter and the component. The measurement of resistance is almost like the measurement of voltage. The ohmmeter is connected parallel to the consumer. The circuit needs to be open! Meaning no current flow possible! Electrical Energy and Power Definition Electrical Energy As we already know, power is the energy per time: \ [\$\$P = \\frac{E}{t} = \\frac{q\*V}{t} = \\frac{q}{t}\*V = I\*V\$\$]{.math.display}\ If we use the definition of resistance, we can get also the relations: \ [\$\$P = \\frac{V\^{2}}{R} = I\^{2}R\$\$]{.math.display}\ The SI-unit of power is of course Watt (W). Electrical Energy \ [*E* = *P* \* *t* = *V* \* *I* \* *t*]{.math.display}\ The SI-unit is Joule (J). But it is very common to use kilowatt-hour if electrical energy is taken \ [1 *kWh* = 3.6 \* 10^6^ J]{.math.display}\ Home Electricity Definition Direct and Alternating Current Definition +-----------------------+-----------------------+-----------------------+ | | Direct Current (DC) | Alternating Current | | | | (AC) | +=======================+=======================+=======================+ | Direction of current | Current always flows | Current direction | | | in the same | changes a few times | | | direction, + to -- | per second. | | | | | | | | Frequency = 50 Hz | +-----------------------+-----------------------+-----------------------+ | Voltage |  | | +-----------------------+-----------------------+-----------------------+ | Voltage source | Batteries | Socket | +-----------------------+-----------------------+-----------------------+ | Consumer | Laptop | Light bulb | | | | | | | Phone | Induction stove | | | | | | | TV | | | | | | | | Light bulb | | | | | | | | Vacuum cleaner | | +-----------------------+-----------------------+-----------------------+ Function Socket Definition The current flows through the neutral and line conductor. In a standard socket, the hot terminal has a high electric potential, the neutral terminal has a low electric potential (near ground), and current flows from the hot terminal to the neutral terminal when a circuit is completed. **Neutral line (Nullleiter) (N)** Potential = 0 V   **Line Conductor / Phase (Phase / Aussenleiter) (L)** Mean potential = 230 V Alternates between +- 325 V, Frequency = 50 Hz   **Protective Earth / Ground (PE)** Potential = 0 V Health Risk Definition For living beings: - Death - Muscle cramp - Burns An electric shock can be fatal at current of 30 mA. - electric shock and burns from contact with live parts. - injury from exposure to arcing (when electricity jumps from one circuit to another) - fire from faulty electrical equipment or installations. - explosion caused by unsuitable electrical apparatus. Safety Measures Definition **Circuit Breaker (Fuse)** - Every socket is protected by a circuit breaker, which controls the current and interrupts the circuit if it becomes too high, such as in a short circuit. This prevents fires and damage but does not necessarily protect against electric shocks. Circuit breakers are located in the fuse box. **Residual Current Device (RCD)** -- The RCD controls the current in the line and neutral conductors, ensuring they are equal but flowing in opposite directions. If a leakage current occurs, such as through a person or a faulty ground wire, the RCD shuts off the circuit to prevent electric shock. Since 2010, new sockets must be protected by an RCD, though older houses may not always have them. RCDs are also found in the fuse box or at sockets. **Protective Earth** -- Electrical devices with metallic housings should be connected to the ground conductor. If a live wire touches the housing, it creates a short circuit and triggers the circuit breaker or RCD. Without grounding, the housing could become electrified, posing a serious shock hazard. If a circuit breaker or RCD trips, troubleshooting involves unplugging devices and resetting the switch. If the cause is unclear, an electrician should be contacted. Phase Tester Definition  A phase tester consists of a high value resistor (to reduce the current) and a bulb. If the user closes the circuit via the body a current can flow if a voltage which is bigger than 0V is applied. Therefore the lamp will shine brighter. The phase tester is a measuring instrument that can measure the phase difference and time difference of synchronous signals in the power system.