Question 8.57: A load consisting of a 50-Ω resistor in parallel with a 8-µF......

The Analysis and Design of Linear Circuits [1399573]

A load consisting of a 50-Ω resistor in parallel with a 8-µF capacitor is connected across a current source delivering $i_{\mathrm{S}}(t)$ = 50 cos (2500t) mA. Find the average power delivered to the load.

Step-by-Step

The 'Blue Check Mark' means that this solution was answered by an expert.
Learn more on how do we answer questions.

The load receives the entire current from the source, so we know the magnitude of the load current equals the magnitude of the source current. We can combine the parallel impedances to find the equivalent impedance and then use the real part to compute the average power delivered to the load.

The 'Blue Check Mark' means that either the MATLAB code/script/answer provided in the answer section has been tested by our team of experts; or the answer in general has be fact checked.

Learn more on how do we answer questions.

Script File

clear all
IL = 50e-3;
w = 2500;
R = 50;
C = 8e-6;
ZC = 1/j/w/C;
ZL = 1/(1/R+1/ZC);
PLavg = real(ZL)/2*IL^2
PLavg =
31.2500e-003

P = 31.25 mW.

Related Answered Questions

Question: 8.67

MATLAB efficiently performs phasor calculations with complex numbers, but it can also be used to better visualize the concept of a rotating phasor. Recall that a sinusoidal signal is the real part of a phasor times e^jωt, where the ω term represents a rotation. The following MATLAB code demonstrates ...

Verified Answer:

The solution is presented as the following MATLAB ...

Question: 8.56

A load consisting of a 1-kΩ resistor in series with a 12-µF capacitor is connected across a voltage source vS(t) = 150 cos (377t) V. Find the phasor voltage, current, and average power delivered to the load. ...

Verified Answer:

In this case, the load voltage equals the source v...

Question: 8.55

Given the circuit in Figure P8-55: (a) Use node-voltage or mesh-current analysis to develop a set of matrix equations for the circuit. (b) Use MATLAB to solve the matrix equations and then find the phasor gain K = VO/VS and input impedance ZIN of the circuit. (c) Without using the matrix equations, ...

Verified Answer:

(a) The node-voltage equations are presented below...

Question: 8.22

The circuit in Figure P8-22 is operating in the sinusoidal steady state with vS(t) = VA cos (ωt). Derive a general expression for the phasor response IL and the voltage VO. ...

Verified Answer:

There are several ways to solve this problem. One ...

Question: 8.23

A current source delivering i(t) = 240 cos (500t) mA is connected across a parallel combination of a 1-kΩ resistor and a 2-µF capacitor. Find the steady-state current iR(t) through the resistor and the steady-state current iC(t) through the capacitor. Draw a phasor diagram showing I, IC, and IR. ...

Verified Answer:

This problem can be solved by converting to the ph...

Question: 8.24

The circuit in Figure P8-24 is operating in the sinusoidal steady state with iS(t) = IA cos (ωt). Derive general expressions for the steady-state responses VR and IC. ...

Verified Answer:

This problem can be solved by using current divisi...

Question: 8.54

Find the phasor gain K = VO/VS and input impedance ZIN of the circuit in Figure P8-54. ...

Verified Answer:

Use node-voltage analysis to solve the problem.

Question: 8.53

Find the phasor gain K = VO/VS and input impedance ZIN of the circuit in Figure P8-53. ...

Verified Answer:

Use node-voltage analysis to solve the problem.

Question: 8.52

The dependent source circuit in Figure P8-52 is operating in the sinusoidal steady state with ω = 1 krad/s and µ = 100. Find the phasor gain K = VO/VS and the input impedance ZIN seen by VS. Validate your answer using OrCAD. ...

Verified Answer:

Use node-voltage analysis to determine expressions...

Question: 8.51

Find the phasor input VS in Figure P8-51 when the phasor output is VO = 200 + j100 V. ...

Verified Answer:

The output phasor voltage appears across two eleme...