A constant voltage of 50 V is maintained between the points A and B of the circuit shown in the figure. The current through the b…

Question

A constant voltage of 50 V is maintained between the points A and B of the circuit shown in the figure. The current through the branch CD of the circuit is:

1. A. 1.5 A
2. B. 2.0 A (Correct answer)
3. C. 2.5 A
4. D. 3.0 A

Correct Answer

Option B — 2.0 A

Detailed Solution & Explanation

The correct answer is 2.0 A.

Key Points

• The network is two parallel branches between $A$ and $B$: branch through $C$ has $1\,\Omega$ then $2\,\Omega$; branch through $D$ has $3\,\Omega$ then $4\,\Omega$.
• $R_{AB}=\dfrac{3\times1}{3+1}+\dfrac{2\times4}{2+4}=\dfrac{3}{4}+\dfrac{8}{6}=\dfrac{25}{12}\,\Omega$, so total current $I=\dfrac{50}{25/12}=24$ A.
• Currents: $I_{1\Omega}=\dfrac{3}{4}\times24=18$ A into $C$; $I_{2\Omega}=\dfrac{4}{6}\times24=16$ A out of $C$.
• Junction rule at $C$: $I_{CD}=18-16=2$ A (from $C$ to $D$).