Questions: (12) In the opposite electric circuit, the reading of the voltmeter is (a) 20 V (b) 15 V (c) 5 V (d) 0

Solution Steps

The circuit consists of:

• A 30V battery with zero internal resistance.
• A 20V battery with zero internal resistance.
• Three resistors: two 5Ω resistors and one 3Ω resistor.
• A voltmeter connected across the 3Ω resistor.

The batteries are connected in series but with opposite polarities. Therefore, the net voltage is: \[ 30V - 20V = 10V \]

The two 5Ω resistors are in series, so their combined resistance is: \[ 5Ω + 5Ω = 10Ω \] This 10Ω resistance is in parallel with the 3Ω resistor. The equivalent resistance \( R_{eq} \) is given by: \[ \frac{1}{R_{eq}} = \frac{1}{10Ω} + \frac{1}{3Ω} \] \[ \frac{1}{R_{eq}} = \frac{3 + 10}{30} = \frac{13}{30} \] \[ R_{eq} = \frac{30}{13} \approx 2.31Ω \]

Using Ohm's Law \( V = IR \): \[ I = \frac{V}{R_{eq}} = \frac{10V}{2.31Ω} \approx 4.33A \]

The current through the 3Ω resistor is the same as the total current because it is in parallel with the combined 10Ω resistance: \[ V_{3Ω} = I \times 3Ω = 4.33A \times 3Ω \approx 13V \]

Final Answer