(a) The potential difference applied across a given resistor is altered so that the heat produced per second increases by a factor of $9$ . By what factor does the applied potential difference change?
(b) In the figure shown, an ammeter A and a resistor of $4 Ω$ are connected to the terminals of the source. The emf of the source is $12$ V having an internal resistance of $2 Ω$ . Calculate the voltmeter and ammeter reading.

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Solution

a) Heat generated H= $i^{2} R t$ = $\frac{V^{2} t}{R}$
$\frac{H}{H^{'}} = \frac{1}{9} = \frac{V^{2}}{V^{' 2}}$
$V^{'} = 3 V$
So potential difference also increases by 3 times.
b) The ammeter is connected in series and has negligible resistance.
Total resistance $= 4 + 2 = 6 Ω$
Ammeter reading $= \frac{12}{6} = 2 A$

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