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

Since the potential at \( A \) and \( B \) is the same, no current flows through the middle resistor (30 \( \Omega \)). The two parallel branches consist of: \[ R_1 = 10 \, \Omega + 20 \, \Omega = 30 \, \Omega \] \[ R_2 = 40 \, \Omega \] The equivalent resistance: \[ R_{{eq}} = \frac{R_1 R_2}{R_1 + R_2} = \frac{(30)(40)}{30 + 40} = \frac{1200}{70} = 17.14 \, \Omega \] The total current using Ohm’s law: \[ I = \frac{40V}{17.14} = 2.33 \, A \]