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

I1 < I2

V1 > V2

Step-by-step 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 = (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) = (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) = (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