Question

The value of current \( I \) in the electrical circuit as given below, when the potential at \( A \) is equal to the potential at \( B \), will be _____ A. 

• A. \( 1.0 \)
• B. \( 2.0 \)
• C. \( 0.5 \)
• D. \( 4.0 \)

Hint:

For circuits with equal potential nodes, eliminate the middle resistor and simplify using series-parallel resistance formulas.

Answer 1

The Correct Option is A

Given that the potentials at \( A \) and \( B \) are equal, no current passes through the central 30 \( \Omega \) resistor.
The two parallel branches have resistances: \[ R_1 = 10 \Omega + 20 \Omega = 30 \Omega \] \[ R_2 = 40 \Omega \] The equivalent resistance is calculated as: \[ R_{{eq}} = \frac{R_1 R_2}{R_1 + R_2} = \frac{(30)(40)}{30 + 40} = \frac{1200}{70} = 17.14 \Omega \] Applying Ohm’s law, the total current is: \[ I = \frac{40V}{17.14} = 2.33 A \]