A battery has an e.m.f of 4 V and an internal resistance r. When this battery is connected to an external resistance of 2 Ω, a current of 1 A flows in the circuit. Find the current that flows if the terminals of the battery are connected directly.

• A. 1 A
• B. 2 A
• C. 4 A
• D. infinite

To find the current that flows when the terminals of the battery are connected directly, we first need to determine the internal resistance of the battery.

Calculating Internal Resistance

The formula for the electromotive force (e.m.f) of a battery is given by:

e.m.f = I(R + r)

Where:

• e.m.f = 4 V
• I = current (1 A)
• R = external resistance (2 Ω)
• r = internal resistance

Substituting the known values into the equation:

4 V = 1 A (2 Ω + r)

This simplifies to:

4 = 2 + r

Thus, the internal resistance r is:

r = 4 - 2 = 2 Ω

Finding the Short-Circuit Current

When the terminals of the battery are connected directly, the external resistance is 0 Ω. The total resistance in the circuit is just the internal resistance:

Total Resistance = r = 2 Ω

Using Ohm's Law (V = I × R), we can find the current:

I = e.m.f / R

Substituting the values:

I = 4 V / 2 Ω = 2 A

Final Answer

Therefore, the current that flows when the terminals of the battery are connected directly is 2 A. The correct option is B.