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 [2025]

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Solution

Q.
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 [2025]

1 2.5 A

2 3.0 A

3 1.5 A

4 2.0 A

Ans.
(4)

Let potential at junction $C$ be $x$

   $\frac{x - 50}{1} + \frac{x - 50}{3} + \frac{x - 0}{2} + \frac{x - 0}{4} = 0$

   $12 x - 600 + 4 x - 200 + 6 x + 3 x = 0$

$25 x - 800 = 0$

or    $x = \frac{800}{25} = 32 V$

Current through $1 Ω$ resistance

$I_{1} = \frac{50 - 32}{1} = 18$ $A$

Current through $2 Ω$ resistance

   $I_{2} = \frac{32 - 0}{2} = 16 A$

$∴$ Current through branch CD is

   $I_{C D} = I_{1} - I_{2} = 18 - 16 = 2 A$

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