Question 1

Q1: A 100 Ω resistor is connected to a 220 V, 50 Hz ac supply. (a) What is the rms value of current in the circuit? (b) What is the net power consumed ove...

Accepted Answer

Given:    Resistance, R = 100 Ω    RMS voltage, V = 220 V    Frequency, f = 50 Hz (a) The rms value of current in the circuit The relation between rms voltage (V), rms current (I), and resistance (R) for a resistive circuit is given by Ohm's law, similar to a DC circuit: V = I R Therefore, the rms c...

Question 2

Q2: (a) The peak voltage of an ac supply is 300 V . What is the rms voltage? (b) The rms value of current in an ac circuit is 10 A . What is the peak curr...

Accepted Answer

(a) RMS voltage from peak voltage Given:    Peak voltage, vₘ = 300 V The relationship between the root mean square (rms) voltage (V) and the peak voltage (vₘ) is: V = vₘ / √2 V = 300 V / 1.414 ≈ 212.1 V The rms voltage is approximately 212.1 V. (b) Peak current from rms current Given:    RMS current...

Question 3

Q3: A 44 mH inductor is connected to 220 V, 50 Hz ac supply. Determine the rms value of the current in the circuit.

Accepted Answer

Given:    Inductance, L = 44 mH = 44 × 10⁻³ H    RMS voltage, V = 220 V *   Frequency, f = 50 Hz First, we need to calculate the inductive reactance (Xₗ) of the circuit. Inductive reactance is the opposition offered by an inductor to the flow of alternating current. The formula for inductive reactan...

Question 4

Q4: A 60 μF capacitor is connected to a 110 V, 60 Hz ac supply. Determine the rms value of the current in the circuit.

Accepted Answer

Given:    Capacitance, C = 60 μF = 60 × 10⁻⁶ F    RMS voltage, V = 110 V *   Frequency, f = 60 Hz First, we need to calculate the capacitive reactance (X꜀) of the circuit. Capacitive reactance is the opposition offered by a capacitor to the flow of alternating current. The formula for capacitive rea...

Question 5

Q5: In Exercises 7.3 and 7.4, what is the net power absorbed by each circuit over a complete cycle. Explain your answer.

Accepted Answer

The net power absorbed by each circuit over a complete cycle is zero. Explanation: The average power (P) dissipated in an AC circuit is given by the formula: P = V I cos(φ) where V is the rms voltage, I is the rms current, and cos(φ) is the power factor. The angle φ is the phase difference between t...

Question 6

Q6: A charged 30 μF capacitor is connected to a 27 mH inductor. What is the angular frequency of free oscillations of the circuit?

Accepted Answer

Given:    Capacitance, C = 30 μF = 30 × 10⁻⁶ F    Inductance, L = 27 mH = 27 × 10⁻³ H This setup describes an LC circuit. The angular frequency (ω₀) of free oscillations in an LC circuit is its natural resonant frequency. It is determined by the values of the inductance (L) and capacitance (C). The...

Question 7

Q7: A series LCR circuit with R = 20 Ω, L = 1.5 H and C = 35 μF is connected to a variable-frequency 200 V ac supply. When the frequency of the supply equ...

Accepted Answer

Given:    Resistance, R = 20 Ω    Inductance, L = 1.5 H    Capacitance, C = 35 μF = 35 × 10⁻⁶ F    RMS voltage of the supply, V = 200 V The problem states that the frequency of the supply equals the natural frequency of the circuit. This is the condition for resonance. At resonance in a series LCR c...

Question 8

Q8: Figure 7.17 shows a series LCR circuit connected to a variable frequency 230 V source. L = 5.0 H, C = 80 μF, R = 40 Ω. (a) Determine the source freque...

Accepted Answer

Given:    Inductance, L = 5.0 H    Capacitance, C = 80 μF = 80 × 10⁻⁶ F    Resistance, R = 40 Ω    RMS source voltage, V = 230 V (a) Source frequency for resonance The circuit is in resonance when the inductive reactance equals the capacitive reactance. The resonant angular frequency (ω₀) is: ω₀ = 1...

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