AC Circuit Power Analysis

What is the definition of instantaneous power, p(t), delivered to any device?

What is the average power (P) for a device in the sinusoidal steady state, given a voltage v(t) = Vm cos(ωt + θ) and current i(t) = Im cos(ωt + φ)?

A current i(t) = 5 cos(100t - 30 degrees) A flows through an impedance Z = 4/60 degrees Ohms. What is the average power delivered to the impedance?

What is the average power delivered to a purely reactive network composed entirely of ideal inductors and capacitors?

Under the maximum power transfer theorem for sinusoidal steady state, a Thévenin source with impedance Zth = Rth + jXth delivers maximum average power to what load impedance ZL?

A Thévenin source has Vth = 100/0 degrees V rms and Zth = 50 + j20 Ohms. What load impedance ZL is required to absorb maximum average power?

How is the effective value of a periodic current, Ieff, defined in relation to the average power P delivered to a resistor R?

What is the effective (rms) value of the sinusoidal voltage v(t) = 170 cos(377t) V?

What is the apparent power, and in what units is it measured?

A load draws an average power of 1200 W from a 240 V rms source. If the apparent power is 1500 VA, what is the power factor?

What does a 'lagging' power factor signify about a load?

Complex power S is defined as Veff * Ieff*. If S = P + jQ, what is Q?

An industrial motor is operating at 50 kW with a lagging power factor of 0.8. What is the reactive power (Q) required by the motor?

The same motor from the previous question (50 kW, 0.8 lagging PF) needs its power factor corrected to 0.95 lagging. What is the complex power of the corrective device that must be added in parallel?

If a current i(t) = (4 cos(10t) + 3 cos(20t)) A is flowing through a 2 Ohm resistor, what is the average power absorbed?

If a current i(t) = (4 cos(10t) + 3 cos(10t)) A is flowing through a 2 Ohm resistor, what is the average power absorbed?

A voltage source v(t) = 40 + 60u(t) V is in a series circuit with a 5 microfarad capacitor and a 200 Ohm resistor. What is the power absorbed by the resistor at t=1.2 ms?

What is the physical interpretation of reactive power, Q?

How is the effective value of a current composed of several sinusoids of different frequencies, I_eff, calculated from the effective values of its components (I_1eff, I_2eff, etc.)?

Calculate the effective value of the periodic voltage v(t) = 6 cos(25t) + 5 sin(30t) + 4 V.

The power triangle is a graphical representation of complex power. If the power triangle for a load lies in the first quadrant, what does this signify?

A load is supplied by a 60 V rms source. The resulting current is 12 A rms and the average power delivered is 288 W. What is the apparent power?

For the circuit in Example 11.4, with two sources and three passive elements, the average power absorbed by the two reactive elements (the inductor and capacitor) is stated to be zero. Why is this?

What is the primary reason an electric utility company might penalize a large industrial customer for having a low power factor?

A phasor voltage V = 115 * sqrt(2) / 45 degrees V is applied to an impedance Z = 16.26 / 19.3 degrees Ohms. The angular frequency is 50 rad/s. What is the average power?

The complex power delivered to a load is S = 500 + j300 VA. What is the power factor of this load?

A current I = (2 + j5) A rms flows into an impedance of 6/25 degrees Ohms. What is the average power delivered?

If a load impedance is Z = 8 - j11 Ohms, what is the nature of its power factor?

The instantaneous power in a sinusoidal steady-state circuit is given by p(t) = P + Pcos(2ωt + β). What does the constant term P represent?

For a standard North American household outlet providing a sinusoidal voltage of 115 V, what does the value '115 V' represent?

A load has a complex power of S = 100 - j50 VA. Which statement is true?

What is the average power absorbed by a 2 Ohm resistor if the current is i(t) = -cos(10t) A?

What is the relationship between the peak amplitude (Im) and the effective value (Ieff) for a sinusoidal current?

A load with impedance ZL = 8 - j11 Ohms has a current I = 5/20 degrees A (peak) flowing through it. What is the average power delivered to this load?

If a circuit has a complex power S = 1000/30 degrees VA, what is the average power P?

Which formula correctly relates average power P to effective (rms) voltage and current?

A load is found to have a power factor of 0.7 leading. What type of element is dominant in the load?

In the power triangle, the three sides represent P, Q, and |S|. What trigonometric relationship defines the power factor angle θ?

The instantaneous power delivered to a circuit is p(t) = 500 + 800cos(200t + 30 degrees) W. What is the average power P?

In Example 11.8, two loads are connected to a 60 V rms source, resulting in a total current of 12 A rms and a total average power of 432 W. What is the power factor of the combined loads?

A current i(t) = 2 - sin(10t) mA flows through a 1 kOhm resistor. What is the effective value of this current?

If a load absorbs 100 W of average power and has a power factor of 0.5 lagging, what is its apparent power?

A phasor current I = 2/-60 degrees A is applied to an impedance Z. The average power is 2 W. If the voltage is v(t) = 4cos(πt/6) V, what is the impedance Z?

Why is the term 'quadrature power' sometimes used for reactive power Q?

The complex power supplied to a load is S. What does the magnitude of S, |S|, represent?

A load is characterized by an impedance Z = 15 + j20 Ohms. A voltage of 100 V rms is applied. What is the average power dissipated by the load?

If a load is purely resistive, what is its power factor?

The average power formula for a resistor using effective voltage is P = V_eff^2 / R. When is it incorrect to use this formula?

For a circuit to deliver maximum average power to a 100 Ohm resistive load, what should the Thévenin equivalent impedance of the source be?

A sinusoidal voltage source vs = 8 sin(200t) V is connected across a 4 Ohm resistor. What is the average power absorbed by the resistor?