Question

In the given circuit, calculate the

(i) Effective resistance between A and B

(ii) Current through the circuit and

(iii)Current through $3\Omega$ resistor.

Answer 1

$\left(i\right)$ Finding effective resistance between A and B

$\left(ii\right)$ Current through the circuit $\left(I\right)$

$\left(iii\right)$ Current through $3\omega$ resistor

$\left(i\right)$ Equivalent resistance$=$

$\frac{12\times 8}{12+8}+\frac{12\times 8}{12}=\frac{12\times 8}{12+8}+\frac{4\times 6}{4+6}=\frac{12\times 8}{20}+\frac{4\times 6}{10}=\frac{12\times 2}{5}+\frac{2\times 6}{5}=\frac{24}{5}+\frac{12}{5}=\frac{24}{5}\omega \frac{1}{\frac{24}{5}}+\frac{1}{3}+\frac{1}{3}=\frac{5}{24}+\frac{1}{3}+\frac{1}{3}=\frac{5+8+8}{24}=\frac{21}{24}\therefore R^1=\frac{24}{21}=1.14\omega$

$\left(ii\right)$ Current through the circuit

$I=\frac{12}{1.14}=10.52A$

$\left(iii\right)$ Current through $3\omega$ resistor

$I_1=\frac{12}{3}=4A$