Question

A \(8\ \Omega\) resistor is connected to a battery that has an internal resistance of \(0.2\ \Omega\). If the voltage across the battery, that is the terminal voltage, is \(10\ \text{V}\), then the emf of the battery is

• A. \(10.15\ \text{V}\)
• B. \(10.20\ \text{V}\)
• C. \(10.25\ \text{V}\)
• D. \(9.80\ \text{V}\)

Hint:

For a battery delivering current, \[ E=V+Ir, \] where \(V\) is terminal voltage and \(r\) is internal resistance. The emf is greater than terminal voltage during discharge.

Answer 1

The Correct Option is C

Step 1: Find current from terminal voltage and external resistance.
\( I = \frac{V_{terminal}}{R} = \frac{10}{8} = 1.25\text{ A} \).

Step 2: Find EMF.
\( E = V_{terminal} + Ir = 10 + 1.25\times0.2 = 10 + 0.25 = 10.25\text{ V} \)

\[ \boxed{E = 10.25\text{ V}} \]