Question:
Which one of the following is the correct equation for the electric circuit shown?
Which one of the following is the correct equation for the electric circuit shown?
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Shortcut:
In KVL → Battery = sum of voltage drops
Drops are always negative terms in loop equation
Updated On: May 8, 2026
- $E_1 - (i_1 + i_2)R + i_1 r_1 = 0$
- $E_1 - (i_1 + i_2)R - i_1 r_1 = 0$
- $E_2 - i_2 r_2 - E_1 - i_1 r_1 = 0$
- $E_2 - (i_1 + i_2)R + i_2 r_2 = 0$
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The Correct Option is B
Solution and Explanation
Step 1: Identify currents
From the diagram:
• Current in middle branch = $i_1$
• Current in bottom branch = $i_2$
• Current through top resistor $R$ = $i_1 + i_2$
Step 2: Apply Kirchhoff’s Voltage Law (KVL)
Consider loop containing $E_1$, $r_1$, and $R$. Traversing the loop:
• Gain from battery = $+E_1$
• Drop across resistor $R$ = $(i_1 + i_2)R$
• Drop across $r_1$ = $i_1 r_1$
Step 3: Write KVL equation
\[ E_1 - (i_1 + i_2)R - i_1 r_1 = 0 \] Conclusion:
This matches option (B). Final Answer: Option (B)
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