Questions: Exercise 2 In the above circuit: 1. Find the voltage across and the current through each component 2. Prove that the power generated = power absorbed 3. Deduce the readings of the voltmeters

Solution Steps

The two 25Ω resistors are in parallel, so their equivalent resistance is given by: \( \frac{1}{R_{eq}} = \frac{1}{25} + \frac{1}{25} = \frac{2}{25} \) \( R_{eq} = \frac{25}{2} = 12.5 \Omega \)

The 1Ω resistor is in series with the 12.5Ω equivalent resistance, and this combination is in series with the 2Ω resistor. So:

\( R_{series1} = 1 + 12.5 = 13.5 \Omega \)

This \( R_{series1} \) is in parallel with 30Ω. \( \frac{1}{R_{parallel}} = \frac{1}{13.5} + \frac{1}{30} = \frac{30+13.5}{13.5 \cdot 30} \) \( R_{parallel} = \frac{405}{43.5} \approx 9.31 \Omega \)

Finally, the equivalent resistance of the circuit is formed by summing this parallel combination with the 2Ω resistor connected in series. \( R_{total} = 2 + \frac{405}{43.5} = 2 + 9.31 = 11.31 \Omega \)

The total current in the circuit can be found using Ohm's law with the 15V source and the total equivalent resistance:

\( I_{total} = \frac{V}{R_{total}} = \frac{15}{11.31} \approx 1.33 A \)

Final Answer