Question

(a) Three resistors $2\Omega ,4\Omega$ and $5\Omega$ are combined in parallel. What is the total resistance of the combination?

(b) If the combination is connected to a battery of emf 20 V and negligible internal resistance, determine the current through each resistor, and the total current drawn from the battery.

Answer 1

(a) For Parallel connection,
$\frac{1}{R_p}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}$
$\frac{1}{R_p}=\frac{1}{2}+\frac{1}{4}+\frac{1}{5}$
$\frac{1}{R_p}=\frac{10+5+4}{20}$
$R_p=\frac{20}{19}\Omega$

(b) $R_1=2\Omega ,R_2=4\Omega ,R_3=5\Omega$

$I_1=\frac{V}{R_1}=20/2=10A$
$I_2=\frac{V}{R_2}=20/4=5A$
$I_3=\frac{V}{R_3}=20/5=4A$
Total current = $I_1+I_2+I_3=19A$