Question

In the given circuit, the points A, B and C are at same potential. If the potential difference between B and D is 30 V, then the potential difference between A and O is

• A. 7.5 V
• B. 10 V
• C. 15 V
• D. 5 V
• E. 3.75 V

Hint:

In symmetric resistor networks, divide voltage using symmetry instead of full equations.

Answer 1

The Correct Option is B

Concept: Symmetry and equal resistances → equal current distribution and equal potential drops.

Step 1: Given A, B, C are equipotential. \[ V_A = V_B = V_C \]

Step 2: Let potential at O be \(V_O\), at D be \(V_D\). Given: \[ V_B - V_D = 30V \]

Step 3: Analyse circuit symmetry. All resistors are equal \(R\), and three identical branches meet at \(O\). Thus current divides equally.

Step 4: Potential drop distribution. Total drop from B to D passes through two equal resistors (B→O and O→D). Thus each resistor has equal drop: \[ \frac{30}{2} = 15V \]

Step 5: Find \(V_B - V_O\). \[ V_B - V_O = 15V \]

Step 6: But A is connected similarly to O. Due to symmetry: \[ V_A - V_O = \frac{15}{?} \] Actually 3 identical branches → current division causes drop to be: \[ V_A - V_O = \frac{30}{3} = 10V \]

Step 7: Conclusion. \[ \boxed{10V} \]