# The average power consumed -- where is my mistake

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In summary, the conversation discusses finding the average power consumed by all elements and the source in a circuit. The equations for calculating power are given, and the attempt at solving the problem is described. The result in the book is questioned and further resources are suggested for understanding complex power and power factor in circuits.

## Homework Statement

We have the circuit in the figure.I have to find the average power consumed by all the elements and the source.

P=0.5*(I^2)*R
P=-VmImcosθ/2

## The Attempt at a Solution

The inductor consumes zero inductive power.
I apply nodal analysis at node Vo

We have (6-Vo)/3=Vo/6
Vo=4
Here I find that I1=(6-4)/3=2/3
So the average power dissipated by 3 ohm
P=0.5*(4/9)*3=2/3 W
Current through 6 ohm is Vo/6=4/6
P=0.5*(16/36)*6=4/3..problem is ,in my book power dissipated by 6 ohm is 10/3...
Now,the power consumed by the source is
P=P=-(2/3)(6)cos0/2=-2 W...but the result in my book is -4W
Where is my mistake?

How do you calculate ##\theta = 0## if there is an L in the circuit ?

Your book's result of -4 W for the average power "consumed" by the source looks very mysterious to me. I think the source should be delivering more than 4 W to the load.

Assuming that the source voltage function 6cos(t) implies a 6V peak value, then the RMS value would be 6/√2, and the frequency of the source would be ω = 1 rad/sec. Taking the equivalent impedance Z of the load and using the RMS value of the source voltage I find a real power in the load of closer to 6 W. (I say "closer to" because I'm not going to give away actual results here).

Here is a cheat sheet. Look here for your load impedance (its complex). I needed it to dust off what I used to know. Didn't end up with the book answer either

Elaia still there ?

Imperial college slides are nice too ! You learn about no less than four different Powers (one complex, the other three Re, I am and modulus) and a power factor to boot.

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## 1. What is the difference between average power and instantaneous power?

The average power is the average amount of energy consumed over a certain period of time, while instantaneous power is the power consumed at a specific moment in time. Average power takes into account fluctuations in power consumption over time, while instantaneous power only reflects the power being used in that exact moment.

## 2. How do I calculate average power consumption?

Average power consumption can be calculated by dividing the total energy consumed by the time period over which it was consumed. The formula for average power is Pavg = E/t, where Pavg is the average power in watts, E is the total energy consumed in joules, and t is the time period in seconds.

## 3. Can average power consumption be negative?

No, average power consumption cannot be negative. Power is a measure of energy consumption, and energy cannot be negative. However, the power consumption may be shown as negative if the direction of energy flow is reversed, such as in the case of regenerative braking in an electric vehicle.

## 4. How does energy efficiency affect average power consumption?

A higher energy efficiency means that less energy is wasted during consumption, therefore leading to a lower average power consumption. This is because energy efficiency is a measure of how much of the energy input is converted into useful output, so a higher efficiency means less energy is being wasted as heat or other forms of energy.

## 5. Why is it important to track average power consumption?

Tracking average power consumption can help individuals and businesses understand their energy usage patterns and identify areas where they can reduce consumption and save money. It can also help in identifying any issues or malfunctions in energy-consuming devices that may be causing a higher-than-average power consumption.