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 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 :
Show Hint
- \( 2.0 \text{ A} \)
- \( 2.5 \text{ A} \)
- \( 3.0 \text{ A} \)
- \( 1.5 \text{ A} \)
The Correct Option is A
Solution and Explanation
To determine the current through branch CD, first simplify the given circuit by identifying the series and parallel combinations of resistors. Then calculate the equivalent resistance between points A and B.
1. Find the equivalent resistance:
Reduce the circuit step by step using the rules for series and parallel combinations until the equivalent resistance between A and B is obtained.
2. Calculate the total current:
Using Ohm's law, the total current supplied by the 50 V source is
\[ I=\frac{V}{R_{\text{eq}}} \]
3. Determine the potential difference across branch CD:
Using Kirchhoff's Voltage Law (KVL) and current division, calculate the voltage across points C and D.
4. Calculate the current through CD:
Applying Ohm's law to branch CD,
\[ I_{CD}=\frac{V_{CD}}{R_{CD}} \]
Substituting the values obtained from the circuit analysis gives
\[ I_{CD}=2.0\ \text{A} \]
Conclusion:
Hence, the current through branch CD is 2.0 A.
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