A battery charger supplies a current of 10 A to charge a storage battery which has an open-circuit voltage of 5.6 V. If the voltmeter connected across the charger reads 6.8 V, what is the internal resistance of the battery?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( 0.12\,\Omega \)
While a battery is being charged, the charger drives the current into it against its emf. So the voltage across its terminals is the emf plus the drop across the internal resistance, \( V=\varepsilon+Ir \). The voltmeter across the charger reads this terminal voltage.
\( \varepsilon=5.6\,\mathrm{V} \)
\( V=6.8\,\mathrm{V} \)
\( I=10\,\mathrm{A} \)
The internal resistance is:
\( \begin{aligned} r &= \frac{V-\varepsilon}{I} \\ &= \frac{6.8\,\mathrm{V}-5.6\,\mathrm{V}}{10\,\mathrm{A}} \\ &= 0.12\,\Omega \end{aligned} \)