When a resistor is connected across the terminals of an ac generator (112 V) that has a fixed frequency, there is a current of 0.500 A in the resistor. When an inductor is connected across the terminals of this same generator, there is a current of 0.400 A in the inductor. When both the resistor and the inductor are connected in series between the terminals of this generator, what are (a) the impedance of the series combination and (b) the phase angle between the current and the voltage of the generator?

Question

When a resistor is connected across the terminals of an ac generator (112 V) that has a fixed frequency, there is a current of 0.500 A in the resistor. When an inductor is connected across the terminals of this same generator, there is a current of 0.400 A in the inductor. When both the resistor and the inductor are connected in series between the terminals of this generator, what are (a) the impedance of the series combination and (b) the phase angle between the current and the voltage of the generator?

For a)
I= E/R
0.500A= 112V/R -> R=224 ohms

0.400A= 112V/XL -> XL=280 ohms

Z= sqrt[R^2 + XL^2]
Z= 358.6 ohms
Did I do this correctly?

b) I'm not really sure about phasor diagrams. I know the current will lag the voltage, but I don't know how to determine the phase angle????

Answer 1

Yes, you did it correctly.

In order to understand phasor diagram, read your text book. In a purely inductive load, the current lags voltage by 90 deg. In this case (R+L load)the phase angle will be less than 90 - you can find it out once you read the text.

Answer 2

Yes, you have correctly calculated the impedance of the series combination. The impedance (Z) is given by the formula Z = √(R^2 + XL^2) = √(224^2 + 280^2) = 358.6 ohms.

To determine the phase angle between the current and voltage, you can use the formula tan(θ) = XL/R. Rearranging the formula, you get θ = arctan(XL/R).

Plugging in the values, θ = arctan(280/224) = arctan(1.25) = 51.34 degrees.

Therefore, the phase angle between the current and voltage of the generator is approximately 51.34 degrees.

Answer 3

For part (a), your calculation is correct. The impedance of the series combination is indeed 358.6 ohms.

Now, let's move on to part (b) and determine the phase angle between the current and the voltage of the generator.

In an AC circuit containing both resistance and inductance elements, the current lags behind the voltage because of the inductive reactance. The phase angle, denoted by θ, represents this time lag or phase difference between the current and voltage.

To find the phase angle, we can use the concept of tangent.

Tangent of the phase angle (θ) is equal to the ratio of reactance (XL) to resistance (R).

tan(θ) = XL / R

Therefore,

θ = arctan(XL / R)

Let's substitute the values:

θ = arctan(280 / 224)
θ ≈ 51.3 degrees

So, the phase angle between the current and the voltage is approximately 51.3 degrees.