Question

In the circuits shown below, the readings of the voltmeters and the ammeters will be:

• A. \(V_2>V_1\) and \(i_1=i_2\)
• B. \(V_1=V_2\) and \(i_1>i_2\)
• C. \(V_1=V_2\) and \(i_1=i_2\)
• D. \(V_2>V_1\) and \(i_1=i_2\)

Answer 1

The Correct Option is C

To solve this problem, we need to analyze both circuits.

Circuit 1:

In Circuit 1, the voltmeter \( V_1 \) is connected in parallel with the \( 10 \, \Omega \) resistor.

• The total resistance in the circuit is \( 10 \, \Omega \).
• The voltage across the resistor \( V_1 \) is equal to the source voltage, \( V = 10\, V \), as it is connected directly across the supply and resistor in series.
• Using Ohm's Law, the current \( i_1 \) through the circuit is calculated as:

\( i_1 = \frac{V}{R} = \frac{10}{10} = 1 \, A \)

Circuit 2:

In Circuit 2, the voltmeter \( V_2 \) is connected across another 10 Ω resistor in parallel with the supply.

• The total resistance across the supply is still effectively \( 10 \, \Omega \), considering parallel configuration does not change the effective resistance of any circuit in series with the supply.
• The voltage across the resistor \( V_2 \) is also equal to the source voltage, \( V = 10\, V \).
• The current \( i_2 \) can be determined similarly as:

\( i_2 = \frac{V}{R} = \frac{10}{10} = 1 \, A \)

Conclusion:

• The voltages \( V_1 \) and \( V_2 \) are equal: \( V_1 = V_2 = 10 \, V \).
• The currents \( i_1 \) and \( i_2 \) are also equal: \( i_1 = i_2 = 1 \, A \).

Thus, the correct answer is: \(V_1=V_2\) and \(i_1=i_2\).