Question

The value of current $ I $ in the adjoining circuit will be

• A. \( \frac{1}{45} \, A \)
• B. \( \frac{1}{15} \, A \)
• C. \( \frac{1}{5} \, A \)
• D. \( \frac{1}{10} \, A \)

Hint:

For delta networks, you can use the formulas to convert to star networks and simplify the calculation of equivalent resistance.

Answer 1

The Correct Option is A

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) \( \frac{1}{45} \, A \).