Current Electricity: Class 12

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Questions and Answers

Explain why connecting batteries in series with opposing polarities can result in a lower overall voltage. Use the concept of EMF in your explanation.

When batteries are connected in series with opposing polarities, their EMFs subtract from each other. The total voltage is reduced because the EMF of one battery counteracts the EMF of the other, effectively decreasing the overall potential difference across the series combination.

A circuit has a junction with three wires connected. If 2A flows into the junction through one wire and 1A flows out through another, what is the current flowing through the third wire, and is it flowing into or out of the junction? Explain your answer using Kirchhoff's Current Law.

According to Kirchhoff's Current Law (junction rule), the total current entering a junction must equal the total current leaving it. Therefore, 1A must be flowing out of the junction through the third wire. 2A (in) = 1A (out) + 1A (out)

Describe how Joule's Law relates current, resistance, and time to the amount of heat generated in a resistor. Give an example of a practical application where understanding this relationship is crucial.

Joule's Law states that the heat generated in a resistor is directly proportional to the square of the current ($I^2$), the resistance ($R$), and the time ($t$). Mathematically, this is expressed as $Heat = I^2Rt$. A practical application is in designing fuses, where the fuse is designed to melt and break the circuit when excessive current causes it to overheat, protecting the circuit from damage.

Two light bulbs are rated for the same voltage, but one has a higher power rating. Explain how you would determine which bulb has a lower resistance. What does this tell you about its brightness?

Since $P = V^2/R$, for a fixed voltage, a higher power rating implies a lower resistance. The bulb with the lower resistance will be brighter because it dissipates more power as light and heat. Signup and view all the answers

If two resistors are connected in parallel, how does the total resistance compare to the individual resistances? Using this concept, explain how adding more resistors in parallel affects the overall current drawn from a voltage source.

The total resistance of resistors in parallel is always less than the smallest individual resistance. Consequently, adding more resistors in parallel decreases the overall resistance of the circuit. Because of Ohm's law <code>V=IR</code>, this will allow more total current to flow from a voltage source. Signup and view all the answers

Explain why, even though electrons are constantly moving randomly within a conductor, there is no net current without an external electric field.

Without an external electric field, the random motion of electrons averages out, resulting in no net directional flow of charge. Therefore, there is no net current. Signup and view all the answers

Differentiate between electric current in a conductor and in an electrolyte, with regards to which particles are moving.

In conductors, electric current is primarily due to the movement of electrons. In electrolytes, current is due to the movement of both positive and negative ions. Signup and view all the answers

A wire carries a current that is decreasing over time. If the charge passing a point in the wire is given by $Q(t) = 5t^2 - t + 3$ Coulombs, what is the current at $t = 2$ seconds?

To find the current at $t=2$ seconds, differentiate the function with respect to time: $I(t) = dQ/dt = 10t - 1$. Evaluating at $t = 2$ gives $I(2) = 10(2) - 1 = 19$ Amperes. Signup and view all the answers

Explain how connecting a battery to a conductor leads to electric current.

Connecting a battery establishes an electric field within the conductor, exerting a force on free electrons, causing them to drift towards the positive terminal and creating a net flow of charge, hence an electric current. Signup and view all the answers

What are the factors that make a material a good conductor of electricity, according to the information provided?

A good conductor has many free electrons available to move and carry charge. Also, the positive charges are fixed in a lattice structure which allows the free electrons to carry charge. Signup and view all the answers

If 20 Coulombs of charge pass through a point in a wire in 4 seconds, calculate the electric current in the wire.

Using the formula $I = Q/t$, the current is calculated as $I = 20 \text{ C} / 4 \text{ s} = 5$ Amperes. Signup and view all the answers

The current through a conductor changes over time and is given by the equation, $I(t) = 3t^2 + 2t$, where I is in Amperes and t is in seconds. Determine the total charge that passes through a cross-section of the conductor between $t = 0$ and $t = 2$ seconds.

Integrate the current function with respect to time from 0 to 2 seconds: $Q = \int_{0}^{2} (3t^2 + 2t) dt$. Solving the definite integral: $Q = [t^3 + t^2]_0^2 = (2^3 + 2^2) - (0^3 + 0^2) = 8 + 4 = 12 $ Coulombs. Signup and view all the answers

A student measures a constant current of 2.0 A through a resistor over a period of 5.0 minutes. Calculate the total charge that flowed through the resistor during this time.

First, convert the time to seconds: $5.0 \text{ minutes} * 60 \text{ seconds/minute} = 300 \text{ seconds}$. Then, use the formula $Q = I * t$ to find the charge: $Q = 2.0 \text{ A} * 300 \text{ s} = 600$ Coulombs. Signup and view all the answers

Explain how the drift velocity of electrons in a conductor changes when the cross-sectional area of the conductor decreases, assuming the current remains constant.

When the cross-sectional area decreases, the drift velocity increases to maintain a constant current, as the current density must increase. Signup and view all the answers

Derive the relationship between current density (J), conductivity ($\sigma$), and electric field (E) from Ohm's Law.

Ohm's Law in microscopic form is given by $J = \sigma E$, where J is current density, $\sigma$ is conductivity, and E is electric field. This equation directly relates these three quantities. Signup and view all the answers

Describe what happens to the resistance of a semiconductor as its temperature increases, and explain the underlying cause.

The resistance of a semiconductor decreases with increasing temperature because more electron-hole pairs are generated, increasing the number of charge carriers. Signup and view all the answers

Explain why the electric field inside a conductor is zero when the conductor is in electrostatic equilibrium.

In electrostatic equilibrium, free charges redistribute themselves on the surface of the conductor such that their electric fields cancel out inside the conductor, leading to a net electric field of zero. Signup and view all the answers

If the current through a conductor varies with time as $I(t) = 2t^2 + 3t$, what is the total charge that passes through a cross-section of the conductor between $t = 0$ and $t = 2$ seconds?

The total charge is given by the integral of the current with respect to time: $Q = \int_0^2 (2t^2 + 3t) dt = [\frac{2}{3}t^3 + \frac{3}{2}t^2]_0^2 = \frac{16}{3} + 6 = \frac{34}{3}$ Coulombs. Signup and view all the answers

How does the average time between collisions ($\tau$) for electrons in a conductor change as the temperature of the conductor increases, and how does this affect the resistance?

As temperature increases, the average time between collisions ($\tau$) decreases because electrons collide more frequently with the vibrating atoms. This decrease in $\tau$ leads to an increase in resistance. Signup and view all the answers

Define the term 'mobility' in the context of electron transport in conductors and provide its formula.

Mobility ($\mu$) is the drift velocity per unit electric field. The formula is $\mu = v_d/E$, where $v_d$ is drift velocity and $E$ is the electric field. Signup and view all the answers

Consider a circuit with two resistors, $R_1$ and $R_2$, connected in series to a voltage source V. If $R_1 > R_2$, which resistor dissipates more power?

In a series circuit, the current is the same through both resistors. Since power $P = I^2R$, the resistor with the larger resistance ($R_1$) dissipates more power. Signup and view all the answers

Explain the difference between EMF and terminal voltage of a battery, and under what condition are they equal?

EMF is the electromotive force, the potential difference when no current is flowing. Terminal voltage is the actual voltage across the battery's terminals when current is flowing. They are equal when the internal resistance is zero or when no current is drawn (open circuit). Signup and view all the answers

Given a conductor with a non-uniform cross-sectional area, explain why the current remains constant throughout the conductor even though the drift velocity changes.

The current remains constant because the charge flow rate must be consistent throughout the conductor to avoid charge accumulation, even though the drift velocity adjusts according to the changing cross-sectional area. Signup and view all the answers

Describe how the temperature coefficient of resistance ($\alpha$) affects the resistance of a material as temperature changes, and explain what a negative value of $\alpha$ implies.

The temperature coefficient of resistance ($\alpha$) quantifies the change in resistance per degree Celsius. A negative value of $\alpha$ implies that the resistance decreases as temperature increases, which is typical for semiconductors. Signup and view all the answers

What is the role of internal resistance in a battery, and how does it affect the battery's performance when delivering current to a circuit?

Internal resistance is the resistance within the battery itself. It causes a voltage drop inside the battery when current flows, reducing the terminal voltage and the power delivered to the external circuit. Signup and view all the answers

Derive the formula for the equivalent resistance of two resistors, $R_1$ and $R_2$, connected in parallel.

For resistors in parallel, $\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2}$. Solving for $R_{eq}$ gives $R_{eq} = \frac{R_1 R_2}{R_1 + R_2}$. Signup and view all the answers

Explain how the application of a battery to a conductor leads to a non-zero drift velocity of electrons, starting from the electrons' random motion.

Without a battery, electrons move randomly with zero net velocity. Applying a battery creates an electric field, which exerts a force on the electrons. This force causes them to accelerate, but collisions with atoms cause them to move with an average drift velocity toward the positive terminal. Signup and view all the answers

A battery is connected to a circuit. Describe the energy conversion process that occurs within the battery.

Inside the battery, chemical energy is converted into electrical energy through chemical reactions between the electrolyte and electrodes, which creates a potential difference that drives current through the circuit. Signup and view all the answers

Flashcards

Series Battery Configuration

Batteries connected end-to-end. Total voltage is the sum of individual voltages.

Kirchhoff's Current Law (KCL)

The sum of currents entering a junction equals the sum of currents leaving it. Net Current = 0