Question 1.SGPYQ.7: In the given figure, the value of R is (a) 10 Ω (b) 18 Ω (c)......

The equivalent circuit is

Applying nodal analysis at V:

\begin{aligned} & =\frac{V-100}{14}+\frac{V}{2}+\frac{V-40}{1}=0 \\ & V-100+7 V+14 V-560=0 \\ & V=\frac{660}{22}=30  V \end{aligned}

Current through 14 Ω and 1 Ω resistors

\begin{aligned} & I_2=\frac{100-30}{14}=\frac{70}{14}=5  A \\ & I_1=\frac{40-30}{1}=10  A \end{aligned}

Therefore, current through R is 5 A (as 10 = 5 + 5)
So,

\begin{gathered} \frac{100-40}{R}=5 \\ R=\frac{60}{5}=12  \Omega \end{gathered}