A battery has an internal resistance that is five times the external resistance connected across it. If the voltage across the battery terminals is 10 V, the emf of the battery is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 60 V
The current in the circuit is \( I=E/(R+r) \). The terminal voltage is the potential difference across the external resistance, \( V=IR \); the rest of the emf is used up inside the battery as \( Ir \).
With \( r=5R \), the terminal voltage is:
\( \begin{aligned} V &= IR \\ &= \frac{ER}{R+5R} \\ &= \frac{E}{6} \end{aligned} \)
Therefore, the emf is:
\( \begin{aligned} E &= 6V \\ &= 6\times10\,\mathrm{V} \\ &= 60\,\mathrm{V} \end{aligned} \)