Question

In the given electrical network, the correct equation for the loop 'ABEFA' is

• A. \( E_1 - I_1(R_1 + R_2 + R_3) - I_2 R_3 = 0 \)
• B. \( E_1 - I_1(R_1 - R_2 + R_3) + I_2 R_3 = 0 \)
• C. \( E_1 - I_1(R_1 + R_2 + R_3) + I_2 R_3 = 0 \)
• D. \( -E_1 + I_1(R_1 + R_2 + R_3) - I_2 R_3 = 0 \)

Hint:

Kirchhoff's Voltage Law is essential in solving circuits, as it allows us to write equations for loops in terms of voltages and resistances.

Answer 1

The Correct Option is C

Step 1: Apply Kirchhoff's Voltage Law (KVL).
According to Kirchhoff’s Voltage Law (KVL), the sum of the potential differences (voltage) around any closed loop in a circuit must equal zero. The equation should account for all the voltages (emf sources and voltage drops across resistors) in the loop.
Step 2: Analyzing the components.
The equation for the loop 'ABEFE' involves the potential drop across the resistors and the emf sources. The correct equation is: \[ E_1 - I_1(R_1 + R_2 + R_3) + I_2 R_3 = 0 \] where \( I_1 \) and \( I_2 \) are the currents, and \( R_1, R_2, R_3 \) are the resistances in the loop.
Step 3: Conclusion.
Thus, the correct equation is \( E_1 - I_1(R_1 + R_2 + R_3) + I_2 R_3 = 0 \), corresponding to option (C).