Question

In the given circuit find the current through $6\Omega$ resistance

• A. $10A$
• B. $7A$
• C. $25A$
• D. $30A$

Answer 1

The correct option is A

$10A$

Step 1: Given data

The resistances are

$$\begin{gathered} R_1=20\Omega \\ {R}_2=5\Omega \\ {R}_3=6\Omega \end{gathered}$$

The voltage of the DC battery shown is:

$$\begin{gathered} V_1=140V \\ {V}_2=90V \end{gathered}$$

Step 2: Take the voltage of the junction a be $V$ , then apply Kirchhoff's Current Law (KCL) at the following junction.

Apply KCL, at point a,

$\begin{array}{c}\frac{V-140}{20}+\frac{V-0}{6}+\frac{V-90}{5}=0\\ \frac{3(V-140)+10V+12(V-90)}{60}=0\\ 3V-420+10V+12V-1080=0\\ 25V-1500=0\\ 25V=1500\\ V=\frac{1500}{25}\\ V=60\end{array}$

Step 3: Use the formula $I=\frac{V}{R}$ to find the current through $6\Omega$,

The current passing through $6\Omega$ is given by

$\begin{array}{c}I=\frac{V_a-V_b}{R}\\ =\frac{V-0}{R}\\ =\frac{60}{6}\\ =10A\end{array}$

Hence, the correct option is (A).