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  4. Two identical wires are first connected in series and then in parallel. The amount of heat produced in both the conditions are in the ratio of:

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Q. Two identical wires are first connected in series and then in parallel. The amount of heat produced in both the conditions are in the ratio of:

BHUBHU 2004

Solution:

Resistance in series combination is more than resistance in parallel combination.
The amount of heat produced across a wire when current $i$ is
$H=i^{2} R t$
Where $R$ is resistance of wire.
In series equivalent resistance is
$R_{s}=R+R=2 R$
In parallel, equivalent resistance is
$R_{p}=\frac{R}{2}$.
$\therefore \frac{H_{s}}{H_{p}}=\frac{2 R}{R / 2}=4 $
$\therefore H_{s}: H_{p}=4: 1$