The value of current $ I $ in the adjoining circuit will be
The value of current $ I $ in the adjoining circuit will be
Show Hint
- \( \frac{1}{45} \, A \)
- \( \frac{1}{15} \, A \)
- \( \frac{1}{5} \, A \)
- \( \frac{1}{10} \, A \)
The Correct Option is A
Solution and Explanation
Step 1: Analyze the circuit.
We are given a triangle circuit with three resistors, each of resistance \( 30 \, \Omega \), and a voltage source of 2 V.
Step 2: Use Ohm’s Law to find the current.
To find the current, first calculate the total equivalent resistance of the circuit. The three resistors form a delta network. First, calculate the equivalent resistance of the delta network.
Next, apply Ohm’s law \( I = \frac{V}{R} \), where \( V = 2 \, \text{V} \) and \( R_{\text{eq}} \) is the equivalent resistance. \[ R_{\text{eq}} = 90 \, \Omega \quad \text{(after simplifying the network of resistors)} \] Then, the current is: \[ I = \frac{V}{R_{\text{eq}}} = \frac{2}{90} = \frac{1}{45} \, A \]
Step 3: Conclusion.
Thus, the current \( I \) in the circuit is \( \frac{1}{45} \, A \).
Conclusion:
The correct answer is (A) \( \frac{1}{45} \, A \).
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