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1. An ordinary household outlet of 110 V rms at 60 Hz is connected to a series circuit consisting of an 8 Ω resistance, 0.0531 H inductance, and 189.7 μF capacitance. Calculate the complex power.
- A. 968 + j726
- B. 8.8 + j6.6
- C. 1210 + j36.87
- D. 560 + j915

2. An AC source of 200 V rms supplies active power of 600 W and reactive power of 800 VAR. The rms current drawn from the source is:
- A. 10 A
- B. 5 A
- C. 3.75 A
- D. 5 A

3. A resistance and a condenser are connected in series across 220 V, 60 Hz mains. What is the capacitance of the circuit when it is adjusted to take 250 watts at a power factor of 0.20?
- A. 69.9 μF
- B. 66.9 μF
- C. 56.8 μF
- D. 37.9 μF

4. A pure inductance of 318 mH is connected in series with a pure resistance of 75 Ω. The circuit is supplied from a 50 Hz source and the voltage across the 75 Ω resistance is found to be 150 V. Calculate the supply voltage.
- A. 220 V
- B. 230 V
- C. 240 V
- D. 250 V

5. A cosine wave function has a phase angle of −26°, a period of 4.19 ms, and a magnitude of 1.41 mA at t=0.826 ms. Determine the maximum value of this wave.
- A. 1.732 mA
- B. 2 mA
- C. 4.32 mA
- D. 3 mA

6. A three-branch parallel circuit, with Z₁ = 25/15° ohms, Z₂ = 15/60° ohms, and Z₃ = 15/90° ohms, has an applied voltage v = 339.4∠30° V. Determine the total apparent power.
- A. 4291 VA
- B. 4402 VA
- C. 5281 VA
- D. 5012 VA

7. A 0.143 H inductor is connected in series with a variable capacitor to a 208 V, 400-cycle source. For what value of capacitance will the current be 1.04 A lagging?
- A. 2.5 μF
- B. 3.8 μF
- C. 1.2 μF
- D. 4.5 μF

8. A unity power factor single-phase load of 1794 watts is connected in parallel with another single-phase load of 1656 watts operating at a lagging power factor of 0.6. If the line voltage is 115 V, calculate the total current.
- A. 35.7 A
- B. 33.8 A
- C. 39.6 A
- D. 30.5 A

Answer :

1. To calculate the complex power in a series circuit, we need to find the total impedance (Z) first.
- The resistance (R) is given as 8Ω.
- The inductance (L) is given as 0.0531H.
- The capacitance (C) is given as 189.7μF.

2. The impedance (Z) in a series circuit can be calculated using the formula: Z = √(R^2 + (XL - XC)^2), where XL is the inductive reactance and XC is the capacitive reactance.
- XL can be calculated as 2πfL, where f is the frequency (60 Hz) and L is the inductance.
- XC can be calculated as 1/(2πfC), where C is the capacitance.
3. Once we find the impedance (Z), the complex power (S) can be calculated using the formula: S = V^2/Z, where V is the voltage (110 V).
4. Now let's calculate the values step by step:
- XL = 2πfL = 2π * 60 * 0.0531 = 20.018 Ω
- XC = 1/(2πfC) = 1/(2π * 60 * 0.1897 * 10^-3) = 53.091 Ω
- Z = √(R^2 + (XL - XC)^2) = √(8^2 + (20.018 - 53.091)^2) = 45.22 Ω
- S = V^2/Z = 110^2/45.22 = 268.89 VA
The complex power in a series circuit can be calculated by finding the total impedance (Z) and then using the formula S = V^2/Z, where S is the complex power, V is the voltage, and Z is the impedance. In this case, the given circuit has a resistance of 8Ω, an inductance of 0.0531H, and a capacitance of 189.7μF. We can calculate the impedance by finding the inductive reactance (XL) and the capacitive reactance (XC) using their respective formulas. After finding the impedance, we can substitute the values into the complex power formula to get the answer. The calculated complex power is 268.89 VA.
The complex power in the given series circuit with an 8Ω resistance, 0.0531H inductance, and 189.7μF capacitance is calculated to be 268.89 VA.

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