Question

Two resistors A and B resistance 4 $\Omega and6\Omega$ respectively are connected in parallel. The combination is connected across a 6 volt battery of negligible resistance. Calculate : (i) the power supplied by the battery, and (ii) the power dissipated in each resistor.

Answer 1

V = 6 , $R_1$ = 4 , $R_2$ = 6
Total Resistance
$\frac{1}{R}$ = $\frac{1}{4}$ + $\frac{1}{6}$
$\frac{1}{R}$ = $\frac{3}{12}$+ $\frac{2}{12}$
$\frac{1}{R}$ = $\frac{5}{12}$
R = $\frac{12}{5}$ = 2.4 ohms

(i) Power supplied by battery
P = $\frac{V^2}{R}$
P = $\frac{6\times 6}{2.4}$ = 15 Watt

(ii)
Power dissipated in $R_1$
P = $\frac{V^2}{R}$
P = $\frac{6\times 6}{4}$ = 9 Watt
[ P.d is same across every resistor in Parallel combination ]

Power disspitated in $R_2$

P = $\frac{V^2}{R}$

P = $\frac{6\times 6}{6}$t = 6 Watt