Question

In the given circuit, find the power consumed by the circuit.

• A. $1.07W$
• B. $2.07W$
• C. $3.07W$
• D. $4.07W$

Answer 1

The correct option is B

$2.07W$

Step 1: Given data

$\begin{array}{l}{R}_1=R_2=R_3=4\Omega \\ R_4=R_5=2\Omega \\ R_6=8\Omega \\ r=1\Omega \\ V=2.2V\end{array}$

Step 2: Arrange the resistance by taking junction a and junction b, also separately show the voltage and its internal resistance

Step 3: Find the equivalent resistance of the series combination

Add the resistances which are in series,

$\begin{array}{l}{R}_7=R_2+R_3=8\Omega \\ R_8=R_4+R_5=4\Omega \end{array}$

Step 4: Find the equivalent resistance of the parallel combination:

$\begin{array}{c}\frac{1}{R}=\frac{2+1+2+1}{8}\\ \frac{1}{R}=\frac{6}{8}\\ \frac{1}{R}=\frac{3}{4}\\ R=\frac{4}{3}\Omega \end{array}$

Step 5: Find the equivalent resistance of the series combination

$\begin{array}{c}R+r=\frac{4}{3}+1\\ R_{eqv}=\frac{4+3}{3}\\ R_{eqv}=\frac{7}{3}\Omega \end{array}$

Step 6: Find the power consumed by the circuit, using formula $P=\frac{V^2}{R}$

$\begin{array}{c}P=\frac{{2.2}^2}{\left(\raisebox{1ex}{$7$}\!\left/ \!\raisebox{-1ex}{$3$}\right.\right)}\\ =\frac{4.84\times 3}{7}\\ =2.074\text{W}\end{array}$

Therefore, the power consumed by the circuit is $2.07\text{W}$.

Hence, the correct option is (B).