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 :

• A. \( 2.0 \text{ A} \)
• B. \( 2.5 \text{ A} \)
• C. \( 3.0 \text{ A} \)
• D. \( 1.5 \text{ A} \)

Hint:

Find the potential difference between points C and D (\(V_{CD}\)). Then find the equivalent resistance between C and D by deactivating the source. The current through CD is \(I_{CD} = V_{CD} / R_{eq,CD}\).

Answer 1

The Correct Option is A

Solution:

To determine the current through branch CD, first analyze the circuit using the laws of series and parallel combinations along with Ohm's law.

1. Simplify the circuit:
Reduce the given resistor network by combining the resistors connected in series and parallel wherever applicable to determine the current distribution in the circuit.

2. Find the potential difference across CD:
Using the equivalent circuit and applying Kirchhoff's Voltage Law (KVL), the potential difference across branch CD is obtained.

3. Apply Ohm's Law:
The current through branch CD is calculated using

\[ I_{CD}=\frac{V_{CD}}{R_{CD}} \]

Substituting the values obtained from the circuit analysis,

\[ I_{CD}=2.0\ \text{A} \]

Conclusion:
Hence, the current flowing through branch CD is 2.0 A.