Cells, EMF, and Internal Resistance

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JEE Advanced 2004

LEVELJEE Advanced

In the circuit shown $A$ and $B$ are two cells of same emf $E$ but different internal resistances $r_{1}$ and $r_{2}$ ( $r_{1} > r_{2}$ ) respectively. Find the value of $R$ such that the potential difference across the terminals of cell $A$ is zero, a long time after the key $K$ is closed.

JEE Advanced 2011

LEVELJEE Main

Two batteries of different emfs and different internal resistances are connected as shown. The voltage across $A B$ in volt is

JEE Advanced 2016

LEVELJEE Advanced

Two batteries with emf $12 V$ and $13 V$ are connected in parallel across a load resistor of $10 Ω$ . The internal resistances of the two batteries are $1 Ω$ and $2 Ω$ , respectively. The voltage across the load lies between

Find the emf ( $V$ ) and internal resistance ( $r$ ) of a single battery which is equivalent to a parallel combination of two batteries of emfs $V_{1}$ and $V_{2}$ and internal resistances $r_{1}$ and $r_{2}$ respectively, with polarities as shown in figure

JEE Advanced 1981

LEVELJEE Advanced

In the circuit shown in figure $E_{1} = 3 V$ , $E_{2} = 2 V$ , $E_{3} = 1 V$ and $R = r_{1} = r_{2} = r_{3} = 1 Ω$ . (a) Find the potential difference between the points $A$ and $B$ and the currents through each branch. (b) If $r_{2}$ is short-circuited and the point $A$ is connected to point $B$ , find the currents through $E_{1}, E_{2}, E_{3}$ and the resistor $R$ .

JEE Advanced 2010

LEVELJEE Main

When two identical batteries of internal resistance $1Ω$ each are connected in series across a resistor $R$ , the rate of heat produced in $R$ is $J_{1}$ . When the same batteries are connected in parallel across $R$ , the rate is $J_{2}$ . If $J_{1} = 2.25 J_{2}$ then the value of $R$ in $Ω$ is

JEE Main 2005

LEVELJEE Main

An energy source will supply a constant current into the load, if its internal resistance is

(A)

equal to the resistance of the load

(B)

very large as compared to the load resistance

(C)

zero

(D)

non-zero but less than the resistance of the load

JEE Main 2019

LEVELJEE Main

For the circuit shown with $R_{1} = 1.0Ω, R_{2} = 2.0Ω, E_{1} = 2 V$ and $E_{2} = E_{3} = 4 V$ , the potential difference between the points $a$ and $b$ is approximately (in volt)

Two batteries with emf $12 V$ and $13 V$ are connected in parallel across a load resistor of $10 Ω$ . The internal resistances of the two batteries are $1 Ω$ and $2 Ω$ , respectively. The voltage across the load lies between

(A)

11.6 V

and

11.7 V

(B)

11.5 V

and

11.6 V

(C)

11.4 V

and

11.5 V

(D)

11.7 V

and

11.8 V

JEE Main 2020

LEVELJEE Main

A battery of $3.0 V$ is connected to a resistor dissipating $0.5 W$ of power. If the terminal voltage of the battery is $2.5 V$ , the power dissipated within the internal resistance is

(A)

0.072 W

(B)

0.125 W

(C)

0.50 W

(D)

0.10 W

JEE Main 2019

LEVELJEE Main

To verify Ohm's law, a student connects the voltmeter across the battery as shown in the figure. The measured voltage is plotted as a function of the current and the following graph is obtained If $V_{0}$ is almost zero, then identify the correct statement.

(A)

The emf of the battery is

1.5 V

and its internal resistance is

1.5 Ω

(B)

The value of the resistance

R

1.5 Ω

(C)

The potential difference across the battery is

1.5 V

when it sends a current of

1000 mA

(D)

The emf of the battery is

1.5 V

and the value of

R

1.5 Ω

JEE Main 2020

LEVELJEE Advanced

The series combination of two batteries, both of the same emf $10 V$ , but different internal resistance of $20 Ω$ and $5 Ω$ , is connected to the parallel combination of two resistors $30 Ω$ and $R Ω$ . The voltage difference across the battery of internal resistance $20 Ω$ is zero, the value of $R$ (in $Ω$ ) is ............... .

LEVELJEE Main

Two sources of equal emf are connected to an external resistance $R$ . The internal resistances of the two sources are $R_{1}$ and $R_{2}$ ( $R_{2} > R_{1}$ ). If the potential difference across the source having internal resistance $R_{2}$ is zero, then

(A)

R = \frac{R _{2} \times ( R _{1} + R _{2} )}{( R _{2} - R _{1} )}

(B)

R = R_{2} - R_{1}

(C)

R = \frac{R _{1} R _{2}}{( R _{1} + R _{2} )}

(D)

R = \frac{R _{1} R _{2}}{( R _{2} - R _{1} )}

JEE Main 2020

LEVELJEE Advanced

A torch battery of length $l$ is to be made up of a thin cylindrical bar of radius $a$ and a concentric thin cylindrical shell of radius $b$ is filled in between with an electrolyte of resistivity $ρ$ (see figure). If the battery is connected to a resistance $R$ , the maximum joule's heating in $R$ will takes place for

(A)

R = \frac{ρ}{2 π l} (\frac{b}{a})

(B)

R = \frac{ρ}{2 π l} ln (\frac{b}{a})

(C)

R = \frac{ρ}{π l} ln (\frac{b}{a})

(D)

R = \frac{2 ρ}{π l} ln (\frac{b}{a})

JEE Main 2021

LEVELJEE Main

Two cells of emf $2 E$ and $E$ with internal resistance $r_{1}$ and $r_{2}$ respectively are connected in series to an external resistor $R$ (see figure). The value of $R$ , at which the potential difference across the terminals of the first cell becomes zero is

(A)

r_{1} + r_{2}

(B)

\frac{r _{1}}{2} - r_{2}

(C)

\frac{r _{1}}{2} + r_{2}

(D)

r_{1} - r_{2}

JEE Main 2019

LEVELJEE Main

In the given circuit, an ideal voltmeter connected across the $10 Ω$ resistance reads 2 V. The internal resistance $r$ , of each cell is

(A)

1.5 Ω

(B)

0.5 Ω

(C)

1 Ω

(D)

0 Ω

JEE Main 2021

LEVELJEE Main

In an electric circuit, a cell of certain EMF provides a potential difference of $1.25$ V across a load resistance of $5Ω$ . However, it provides a potential difference of $1$ V across a load resistance of $2Ω$ . The emf of the cell is given by $\frac{x}{10}$ V. Then, the value of $x$ is ......... .

JEE Main 2021

LEVELJEE Main

Five identical cells each of internal resistance $1Ω$ and emf $5 V$ are connected in series and in parallel with an external resistance $R$ . For what value of $R$ , current in series and parallel combination will remain the same ?

(A)

1Ω

(B)

25Ω

(C)

5Ω

(D)

10Ω

JEE Main 2021

LEVELJEE Advanced

In the given figure, the emf of the cell is $2.2 V$ and if internal resistance is $0.6Ω$ . Calculate the power dissipated in the whole circuit

(A)

1.32 W

(B)

0.65 W

(C)

2.2 W

(D)

4.4 W

JEE Main 2021

LEVELJEE Main

A cell $E_{1}$ of emf 6V and internal resistance $2Ω$ is connected with another cell $E_{2}$ of emf 4V and internal resistance $8Ω$ (as shown in the figure). The potential difference across points X and Y is

In the circuit shown, the potential difference between A and B is

A cell of internal resistance $r$ drives current through an external resistance $R$ . The power delivered by the cell to the external resistance will be maximum when

(A)

R = 2 r

(B)

R = r

(C)

R = 0.001 r

(D)

R = 1000 r

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An energy source will supply a constant current into the load, if its internal resistance is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } For the circuit shown with R1​=1.0Ω,R2​=2.0Ω,E1​=2 V and E2​=E3​=4 V, the potential difference between the points a and b is approximately (in volt)

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } In the given circuit, an ideal voltmeter connected across the 10 Ω resistance reads 2 V. The internal resistance r, of each cell is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } In the given figure, the emf of the cell is 2.2 V and if internal resistance is 0.6Ω. Calculate the power dissipated in the whole circuit

In the circuit shown, the potential difference between A and B is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A cell of internal resistance r drives current through an external resistance R. The power delivered by the cell to the external resistance will be maximum when

Two batteries of different emfs and different internal resistances are connected as shown. The voltage across $A B$ in volt is

For the circuit shown with $R_{1} = 1.0Ω, R_{2} = 2.0Ω, E_{1} = 2 V$ and $E_{2} = E_{3} = 4 V$ , the potential difference between the points $a$ and $b$ is approximately (in volt)

In the given circuit, an ideal voltmeter connected across the $10 Ω$ resistance reads 2 V. The internal resistance $r$ , of each cell is

In the given figure, the emf of the cell is $2.2 V$ and if internal resistance is $0.6Ω$ . Calculate the power dissipated in the whole circuit

A cell of internal resistance $r$ drives current through an external resistance $R$ . The power delivered by the cell to the external resistance will be maximum when