Question

Find the change in current (in A) in $8\Omega$ resistor branch if a resistor of $2\Omega$ is added. Also, find percentage error in circuit by compensation theorem.

• A. 0.65 A, 20%
• B. 0.56 A, 11.99%
• C. 0.56 A, 10%
• D. 0.56 A, 11.2%

Answer 1

The correct option is D 0.56 A, 11.2%

By current division rule,
$i=\frac{(3+5)}{(3+5+8)}\times 10=5A$
Compensation circuit,

Here, $V_c=i\times \Delta R=5\times 2=10V$
$i_c=\frac{10}{8+2+3+5}=0.56A$
$\text{Percentage error}=\frac{i_c}{i}\times 100=\frac{0.56}{5}\times 100=11.2\%$
Now,

$i_c^{\prime }=10\times \frac{(3+5)}{(8+2+5+3)}=4.44A$
Change in circuit = $i-i_c^{\prime }$
$=(5-4.44)A$
$=0.56A$