Question

Find the total current that passes through the circuit. Find the heat generated across the each resistor:

Answer 1

Given: a circuit

To find the total current that passes through the circuit and the heat generated across the each resistor

Solution:

Effective resistance of$12\Omega$ and$6\Omega$ in parallel is,

$R_P=\frac{12\times 6}{12+6}⟹R_P=\frac{72}{18}⟹R_P=4\Omega$

The effective resistance of $4\Omega$ and $R_P$ in series is

$R_{eff}=4+R_P=4+4⟹R_{eff}=8\Omega$

Now according to the Ohm's law,

$V=IR⟹I=\frac{V}{R_{eff}}⟹I=\frac{16}{8}⟹I=2A$

Hence $2A$ is the total current that passes through the circuit.

Current through $4\Omega$ is $I_1=2A$

Potential difference across $4\Omega =I_1{R}_1=2\times 4=8V$

Current through $12\Omega$ is $I_2=\frac{8}{12}=0.66A$

Current through $6\Omega$ is $I_3=\frac{8}{6}=1.33A$

(i) Heat generated per second in $4\Omega$ Resistor

$H_1=I_1^2\left(R_1\right)t⟹H_1=2^2\times 4\times 1⟹H_1=16J$

(ii) Heat generated per second in $12\Omega$ Resistor

$H_2=I_2^2\left(R_2\right)t⟹H_2=(0.66{)}^2\times 12\times 1⟹H_2=5.23J$

(iii) Heat generated per second in $6\Omega$ Resistor

$H_3=I_3^2\left(R_3\right)t⟹H_3=(1.33{)}^2\times 6\times 1⟹H_3=10.6J$