Current Electricity — CBSE Class 12 board PYQs

An ammeter and a voltmeter are connected in series to a battery, their readings being $A$ and $V$ respectively. If a resistor is now connected in parallel with the voltmeter, then:

A galvanometer shows full-scale deflection for a current $I_g$. With a shunt $S_1$ it becomes an ammeter of range $(0\text{–}I)$; with a shunt $S_2$ its range becomes $(0\text{–}2I)$. Then $\frac{S_1}{S_2}$ is:

A current of $0.8\text{A}$ flows in a conductor of $40\Omega$ for 1 minute. The heat produced in the conductor will be:

A cell of EMF $E$ is connected across an external resistance $R$. When a current $I$ is drawn from the cell, the potential difference across its electrodes drops to $V$. The internal resistance $r$ of the cell is:

A potentiometer can measure the EMF of a cell because:

Two resistors $R_1$ and $R_2$ of $4\Omega$ and $6\Omega$ are connected in parallel across a battery. The ratio of power dissipated in them, $P_1:P_2$, will be:

How is the drift velocity in a conductor affected by a rise in temperature?

Define the mobility of a charge carrier. What is its relation with relaxation time?

The graph shows the variation of current versus voltage for the material GaAs. Identify the region of
(i) negative resistance and
(ii) where Ohm's law is obeyed.

The graph shows a plot of current versus voltage for a given semiconductor. Identify the region, if any, over which the semiconductor has a negative resistance.

Two identical cells, each of EMF $E$ and negligible internal resistance, are connected in parallel with each other across an external resistance $R$. What is the current through this resistance?

Show, on a graph, the variation of resistivity with temperature for a typical semiconductor.

A wire of resistance $8R$ is bent in the form of a circle. What is the effective resistance between the ends of a diameter AB?

The variation of potential difference $V$ with length $\ell$ for two potentiometers P and Q is shown. Which one would you prefer for comparing the EMFs of two primary cells?

Sketch a graph showing the variation of resistivity of carbon with temperature.

Establish a relation between electric current and drift velocity.

What are superconductors?

Name the temperature for a thermocouple at which its
(i) thermo-emf changes its sign, and
(ii) thermoelectric power becomes zero.

(i) Define the 'temperature coefficient of resistance' of a metal.
(ii) Show the variation of the resistivity of copper with a rise in temperature.
(iii) The resistance of a wire is $10\Omega$ at $27^{\circ }\text{C}$. Find its resistance at $-3^{\circ }\text{C}$, given the temperatu …

Define current density and relaxation time. Derive an expression for the resistivity of a conductor in terms of the number density of charge carriers and the relaxation time.

Explain the principle of working of a metre bridge. Draw the circuit diagram for the determination of an unknown resistance using it.

(a) Two cells of EMF $E_1,E_2$ and internal resistances $r_1,r_2$ are connected in parallel across an external resistance $R$ (the cells supporting each other). Deduce the equivalent EMF and internal resistance.
(b) If the two cells are identical, each of EMF $E=5\text{V}$ and …

Two bulbs are rated $(P_1,V)$ and $(P_2,V)$. If they are connected
(i) in series and
(ii) in parallel across a supply of voltage $V$, find the power dissipated in the two combinations in terms of $P_1$ and $P_2$.

Using Kirchhoff's rules, calculate the current through the $40\Omega$ and $20\Omega$ resistors in the given circuit. \\ \textbf{OR} \\ What is end error in a metre bridge and how is it overcome? The two arms have $R=5\Omega$ and $S$. When $S$ is shunted with an equal resist …

Two electric bulbs P and Q have their resistances in the ratio $1:2$. They are connected in series across a battery. Find the ratio of the power dissipated in them.

A $10\text{V}$ cell of negligible internal resistance is connected in parallel across a battery of EMF $200\text{V}$ and internal resistance $38\Omega$, as shown. Find the current in the circuit.

(a) Define the conductivity of a metallic wire and write its SI unit.
(b) Using the free-electron model, derive the expression for the conductivity of a wire in terms of the number density and the relaxation time, and hence obtain the relation between the current density and the …

Derive the expression for the current density of a conductor in terms of the conductivity and the applied electric field. Explain, with reason, how the mobility of electrons changes when the potential difference applied is doubled at constant temperature.

A resistance $R$ draws current from a potentiometer whose wire AB has total resistance $R_0$; a voltage $V$ is supplied to the potentiometer. Derive an expression for the voltage across $R$ when the sliding contact is at the middle of the wire.

Describe the working principle of a moving-coil galvanometer. Why is it necessary to use
(i) a radial magnetic field and
(ii) a cylindrical soft-iron core? Write the expression for the current sensitivity. Can a galvanometer as such be used for measuring current? Explain.

Two cells of EMF $1.5\text{V}$ and $2.0\text{V}$, having internal resistances $0.2\Omega$ and $0.3\Omega$ respectively, are connected in parallel. Calculate the EMF and the internal resistance of the equivalent cell.

When a $5\text{V}$ potential difference is applied across a wire of length $0.1\text{m}$, the drift speed of the electrons is $2.5\times 10^{-4}{\text{m s}}^{-1}$. If the electron density in the wire is $8\times 10^{28}{\text{m}}^{-3}$, calculate the resistivity of the material …

Two identical cells of EMF $1.5\text{V}$ each, joined in parallel, supply energy to an external circuit of two $7\Omega$ resistances joined in parallel. A high-resistance voltmeter reads the terminal voltage as $1.4\text{V}$. Calculate the internal resistance of each cell.

Use Kirchhoff's rules to obtain the balance condition of a Wheatstone bridge.

A cell of EMF $E$ and internal resistance $r$ is connected across a variable load $R$. Draw the plots of
(i) the terminal voltage $V$ and
(ii) the current $I$ versus $R$. It is found that when $R=4\Omega$ the current is $1\text{A}$, and when $R=9\Omega$ the current is …

Estimate the average drift speed of the conduction electrons in a copper wire of cross-sectional area $2.5\times 10^{-7}{\text{m}}^2$ carrying a current of $2.7\text{A}$. Take the conduction-electron density as $9\times 10^{28}{\text{m}}^{-3}$.

A cell of EMF $E$ and internal resistance $r$ is connected across a variable resistor $R$. Plot a graph of the terminal voltage $V$ versus the current $I$. Using the plot, show how the EMF and the internal resistance of the cell can be determined.

(a) Why are the connections between the resistors in a metre bridge made of thick copper strips?
(b) Why is it generally preferred to obtain the balance point in the middle of the wire?
(c) Which material is used for the metre-bridge wire and why? \\ \textbf{OR} \\ A resistance …

Explain the term 'drift velocity' of electrons in a conductor. Hence obtain the expression for the current through a conductor in terms of the drift velocity. \\ \textbf{OR} \\ Describe briefly, with the help of a circuit diagram, how a potentiometer is used to determine the inte …

Define the current sensitivity of a galvanometer and write its SI unit. The figure shows two circuits, each with a galvanometer and a $3\text{V}$ battery. When the galvanometers show no deflection, obtain the ratio $R_1/R_2$.

A cell of EMF $E$ and internal resistance $r$ is connected to two external resistances $R_1$ and $R_2$ and a perfect ammeter. The current is measured in four cases:
(i) no external resistance;
(ii) with $R_1$ only;
(iii) with $R_1$ and $R_2$ in series;
(iv) with $R_1$ and $R_2$ i …

In a long uniform potentiometer wire AB of constant potential gradient, the null points for two primary cells of EMFs ${\epsilon }_1$ and ${\epsilon }_2$ (connected as shown) are obtained at $120\text{cm}$ and $300\text{cm}$ from A. Find (i) ${\epsilon }_1/{\epsilon }_2$ and …

In the given circuit, taking point A to be at zero potential, use Kirchhoff's rules to determine the potential at point B.

In a metre-bridge experiment the balance point was observed at J with $AJ=\ell$.
(i) If the values of R and X are doubled and then interchanged, what is the new balance point?
(ii) If the galvanometer and the battery are interchanged at the balance position, how is the balance po …

Two heating elements of resistances $R_1$ and $R_2$, when operated at a constant supply voltage $V$, consume powers $P_1$ and $P_2$ respectively. Deduce expressions for the power of their combination when they are connected in
(i) series and
(ii) parallel across the same supply.

Write the principle of working of a potentiometer. Describe briefly, with a circuit diagram, how a potentiometer is used to determine the internal resistance of a given cell.

A cell of EMF $E$ and internal resistance $r$ is connected across a variable resistor $R$. Plot a graph showing the variation of the terminal potential difference $V$ with $R$, and predict from the graph the condition under which $V$ becomes equal to $E$.

Derive an expression for the drift velocity of free electrons in a conductor in terms of the relaxation time.

Calculate the current drawn from the battery in the given network.

A wire of $15\Omega$ resistance is gradually stretched to double its original length. It is then cut into two equal parts, which are connected in parallel across a $30\text{V}$ battery. Find the current drawn from the battery.

(i) State the principle of a metre bridge. (ii) In a metre bridge the balance point is at distance ${\ell }_1$ with resistances R and S. When an unknown resistance $X$ is connected in parallel with S, the balance point shifts to ${\ell }_2$. Find the expression for $X$ in terms of …

In a bridge, with two unknown resistances X and Y inserted, the null point D is $40\text{cm}$ from end A. When a $10\Omega$ resistance is connected in series with X, the null point shifts by $10\text{cm}$. Find the position of the null point when the $10\Omega$ is instead …

Two wires X and Y have the same resistivity, but their cross-sectional areas are in the ratio $2:3$ and their lengths in the ratio $1:2$. They are first connected in series and then in parallel to a DC source. Find the ratio of the drift speeds of the electrons in the two wires i …

The graph shows the variation of the terminal potential difference $V$ across a combination of three cells in series (connected to a resistor) with the current $i$.
(i) Calculate the EMF of each cell.
(ii) For what current $I$ will the power dissipation be maximum?

A cylindrical metallic wire is stretched to increase its length by $5\%$. Calculate the percentage change in its resistance.

State Kirchhoff's rules of current distribution in an electrical network. Using these rules, determine the value of the current in the given circuit.

Write the mathematical relation for the resistivity of a material in terms of the relaxation time, number density, mass and charge of the carriers. Using it, explain why the resistivity of a metal increases and that of a semiconductor decreases with a rise in temperature.

In the given circuit the cells $E_1$ and $E_2$ have EMFs $5\text{V}$ and $9\text{V}$ and internal resistances $0.3\Omega$ and $1.2\Omega$ respectively. Calculate the current flowing through the $3\Omega$ resistance.

Write the mathematical relation between mobility and drift velocity of charge carriers in a conductor. Name the mobile charge carriers responsible for conduction of electric current in
(i) an electrolyte and
(ii) an ionised gas.

You are given $n$ resistors, each of resistance $r$. They are first connected to get the minimum possible resistance and then connected differently to get the maximum possible resistance. Compute the ratio of the minimum to the maximum resistance so obtained.

Draw a circuit diagram using a metre bridge and write the mathematical relation used to determine the value of an unknown resistance. Why cannot such an arrangement be used for measuring very low resistances?

A $10\text{m}$ long potentiometer wire of uniform cross-section and $20\Omega$ resistance is connected in series with a $5\text{V}$ battery and an external resistance of $480\Omega$. An unknown EMF $E$ is balanced at a length of $6.0\text{m}$. Calculate
(i) the potentia …

Draw the $V$–$I$ graph for ohmic and non-ohmic materials. Give one example of each.

How does the resistivity of
(i) a conductor and
(ii) a semiconductor vary with temperature? Give the reason in each case.

Two cells of EMF $1.5\text{V}$ and $2\text{V}$ and internal resistances $1\Omega$ and $2\Omega$ respectively are connected in parallel to pass current in the same direction through an external $5\Omega$ resistor.
(i) Draw the circuit diagram.
(ii) Using Kirchhoff's laws …

Define the term 'resistivity' and write its SI unit. Derive the expression for the resistivity of a conductor in terms of the number density of free electrons and the relaxation time. \\ \textbf{OR} \\ State the principle of a potentiometer. Draw a circuit to compare the EMFs of …

Explain, with the help of a graph, the variation of conductivity with temperature for a metallic conductor.

The circuit shows a potentiometer used to measure a small EMF produced by a thermocouple connected between X and Y. The driver cell C has EMF $2\text{V}$ and negligible internal resistance; the potentiometer wire PQ is $1.00\text{m}$ long with resistance $5\Omega$. The bala …

(a) Draw a circuit diagram of a metre bridge used to determine the unknown resistance $R$ of a wire, and derive the expression for $R$ in terms of the known resistance $S$. (b) What is meant by 'end error' in a metre bridge and how is it corrected? How is the balancing point affe …

(i) Derive an expression for the drift velocity of electrons in a conductor and hence deduce Ohm's law. (ii) A wire whose cross-sectional area increases linearly from one end to the other is connected across a battery of $V$ volts. Which of the following remains constant along th …

(i) Define the term drift velocity. (ii) On the basis of electron drift, derive an expression for the resistivity of a conductor in terms of the number density of free electrons and the relaxation time, and state on what factors the resistivity depends. (iii) Why are alloys like …