Question

Two identical batteries have the same internal resistance. Battery 1 is connected to a resistor R1 and battery 2 to a resistor R2 > R1. Compare the terminal voltage of these batteries and the current they provide. A) V1>V2 and I1>I2
B) V1>V2 and I1 C) V1 D) V1I2
E) V1 Please provide explanation

Answer 1

Answer:

I1 < I2

V1 > V2

Explanation:

Let the EMF of both the batteries is E and the internal resistance of both the cells is r.

The relation between the current and the EMF is given by

$I = \frac{E}{R+r}$

where, R be the resistance connected in the circuit.

the relation between the terminal potential difference and the EMF is given by

V = E - Ir

where, V is the terminal potential difference

If R1 is connected,

The current is given by

$I_{1} = \frac{E}{R_{1}+r}$       .... (1)

The terminal potential difference is given by

$V_{1}=E - I_{1}r$        ..... (2)

If R2 is connected,

The current is given by

$I_{2} = \frac{E}{R_{2}+r}$       .... (3)

The terminal potential difference is given by

$V_{2}=E - I_{2}r$        ..... (4)

As given in the question, R2 > R1

So, by the equation (1) and (3), we get

I1 < I2

and by the equation (2) and (4) ,we get

V1 > V2