# Series LR circuit

• Engineering

## Homework Statement

1)A coil of self inductance of 0.7 Henry is joined in series with a non inductive resistance of 5 ohms. Calculate the wattless and power components as well as total current when connected to a supply of 200 volts at frequency of 50 cycles per second.

## The Attempt at a Solution

It is given in my book that the power component of current = I(1)[cos(theta)]
Where I(1) = Root Mean Square value of total current in the circuit
I think theta is the phase difference between current and voltage in circuit
Also they say that the wattless component of current = I(1)[sin(theta)]
Could somebody please explain, what is the concept behind this?

## Answers and Replies

berkeman
Mentor
I'm not familiar with those exact terms, but I think I can see what they are driving at.

Try this -- plot the complex impedance vector in the complex plane, with the real (resistive) axis on the horizontal and the imaginary (reactive) axis on the vertical. Calculate the complex impedance looking into the series combination of the L and R, and plot that as a vector in this 2-space. The horizontal component is just the resistance, and the vertical component is the reactive impedance of the inductor at that frequency. So if you have the total power as P = |Z| I(1), then it would make sense what they are saying about the cosine component being the portion across the resistor. Does that work out?

I'm not familiar with those exact terms, but I think I can see what they are driving at.

Try this -- plot the complex impedance vector in the complex plane, with the real (resistive) axis on the horizontal and the imaginary (reactive) axis on the vertical. Calculate the complex impedance looking into the series combination of the L and R, and plot that as a vector in this 2-space. The horizontal component is just the resistance, and the vertical component is the reactive impedance of the inductor at that frequency. So if you have the total power as P = |Z| I(1), then it would make sense what they are saying about the cosine component being the portion across the resistor. Does that work out?

I got your point.Thanks buddy. 