Question

Two identical resistors each of resistance $10\Omega$ are connected in turn (i) in series and (ii)in parallel to a battery of $6V$. Calculate the ratio of power consumed in series and parallel combination:

Answer 1

When the two resistors are in series, total resistance = $R_s=10+10=20\Omega$

$I_s=\frac{V}{R}=\frac{6}{20}=0.3A$

When the two resistors are connected in parallel, total resistance :

$\frac{1}{R_p}=\frac{1}{10}+\frac{1}{10}$

$\Rightarrow R_p=5\Omega$

$I_p=\frac{6}{5}=1.2A$

Power = V I

Thus, the ratio of power consumed in series and parallel combination is;

$\frac{P_s}{P_p}=\frac{0.3}{1.2}=0.25$