Question

If two resistors with resistance 5 $\Omega$ and 10 $\Omega$ respectively , are connected to a battery of emf 6V, then determine the strength of the total resistance and current in the circuit when connected in
(a) parallel combination and (b) series combination

Answer 1

Given,

Two resistors with resistances,

$R_1=5\Omega$

$R_2=10\Omega$

Voltage, $V=6V$

In parallel combination,

Equivalent resistance, $R_p$

$\frac{1}{R_p}=\frac{1}{R_1}+\frac{1}{R_2}$

$R_p=\frac{R_1{R}_2}{R_1+R_2}$

$R_p=\frac{5\times 10}{5+10}=3.33\Omega$

Current, $I_p=\frac{V}{R_p}$

$I_p=\frac{6}{3.33}$

$I_p=1.80A$

In series combination,

$R_s=R_1+R_2$

$R_s=5+10$

$R_s=15\Omega$

Current, $I_s=\frac{V}{R_s}$

$I_s=\frac{6}{15}$

$I_s=0.4A$