Question

A battery of 10 V and internal resistance 0.5 Ω is connected in parallel with a battery of 12 V and internal resistance 0.8 Ω. The terminals are connected by an external resistance of 20 Ω. The current flowing through the 20 Ω resistance is:

• A. 0.75 A
• B. 1.74 A
• C. 0.53 A
• D. 1.21 A

Hint:

When multiple batteries are connected in parallel, their equivalent EMF and internal resistance must be calculated before determining the total current in the circuit.

Answer 1

The Correct Option is C

To solve this, we first calculate the equivalent EMF of the parallel combination of the two batteries using the formula: \[ \frac{1}{R_{\text{eq}}} = \frac{1}{R_1} + \frac{1}{R_2} \] Then, we calculate the total current in the circuit, and use Ohm's Law: \[ I = \frac{V_{\text{eq}}}{R_{\text{total}}} \] Where \( V_{\text{eq}} \) is the equivalent EMF, and \( R_{\text{total}} \) is the total resistance, which includes the internal resistance of the batteries and the external resistance.