Question

Two resistors of resistance 4 Ω and 6 Ω are connected in parallel to a cell to draw 0.5 A current from the cell.
a) Draw a labelled diagram of the arrangement.
b) Calculate current in each resistor.

Answer 1

(a) Circuit diagram:
Equivalent resistance of the circuit:
Given,
$R1=4\Omega \text{and}R2=6\Omega$ are in parallel
The resistance of the parallel combination
$\left(R1||R2\right)$ is
$R_{eq}=\frac{R_1{R}_2}{R_1+R_2}=\frac{4\times 6}{4+6}=2.4\Omega$
Emf of the cell:
Resistance of the parallel combination,
$R_{eq}=2.4\Omega$
Current drawn from the cell, $I=0.5A$.
By applying Ohm’s law for $R_{eq}$ ,
$V=I{R}_{eq}=\left(0.5A\right)\times \left(2.4\Omega \right)=1.2V$
(b) Current in each resistor:
The potential difference across both the resistors is same and is equal to the emf of the cell.
Applying Ohm’s law for $R_1=4\Omega$
$V=I_1{R}_1$
Current through the resistor $R_1$
$I_1=\frac{V}{R_1}=\frac{1.2V}{4\Omega }=0.3A$
Applying Ohm’s law for $R_2=6\Omega$
$V=I_2{R}_2$
Current through the resistor $R_2$
$I_2=\frac{V}{R_2}=\frac{1.2V}{6\Omega }=0.2A$