Question

Resistors $R_1$, $R_2$ and $R_3$ having values 5 $\Omega$, 10 $\Omega$, and 30 $\Omega$ respectively are connected in parallel across a battery of 12 volts. Calculate

(a) the current through each resistor

(b) the total current in the circuit and

(c) the total circuit resistance

Answer 1

Here, R₁ = 2 $\Omega$, R₂ = 10 $\Omega$, R₃ = 30 $\Omega$ and V = 12 V

(a) From Ohm’s law, R = $\frac{V}{I}$

Then, I = $\frac{V}{R}$

Putting values, we get, $I_1$ = $\frac{V}{R_1}$ = $\frac{12}{5}$ = 2.4 A

$I_2$ = $\frac{V}{R_2}$ = $\frac{12}{10}$ = 1.2 A

$I_3$ = $\frac{V}{R_3}$ = $\frac{12}{30}$ = 0.4 A

(b) Total current, I = $I_1$ + $I_2$ + $I_3$ = 2.4 + 1.2 + 0.4 = 4 A

(c) From relation, $\frac{1}{R_p}$ = $\frac{1}{R_1}$ + $\frac{1}{R_2}$ + $\frac{1}{R_3}$

Putting values, we get, $R_p$ = 3 $\Omega$