What Determines Maximum Voltage in an RL Circuit with AC Power?

[XenoPhex]

I know this is a simple question but I can't quite figure out how to do this in a combined circuit:

Find the maximum voltage across a resistor R and inductor L with an AC power source of V₀sin(wt). (Note: the resistor is in series with the inductor) I'm trying to figure out the total max voltage and the max voltage for each (if that's even possible).

I'm a bit new to AC circuits so I don't really know how to handle things when dealing with them, so any extra tips outside of how to go about this problem would help immensely.

 

[vk6kro]

If you have an inductor and know its inductance you can work out its reactance at a known frequency by this formula:
XL = 2 * pi * F * L
eg 10000 hz and 1 mH, ZL =62.8 ohms

If this is put in series with a 100 ohm resistor, what would be the resulting impedance?

The easy way is to draw (or imagine) a triangle with R horizontal and XL vertically upward from the end of the resistive line (so it is a right angled triangle) and then draw a hypotenuse on these lines to make a triangle.
This hypotenuse represents the resultant impedance.

Using Pythagoras, Z^2 = R^2 + XL^2
so Z^2 = 100^2 + 62.8^2
from this Z= 118.08 ohms

So if you put 150 volts across the series combination at 10000 Hz the current would be
150 / 118.08 or 1.27 A

This current flows through the coil and the resistor.
Voltage across the resistor = I R = 1.27 * 100 = 127 V
Voltage across the coil = 1.27 * 62.8 = 79.76 V

Note that these add up to more than 150 volts, but their squares add up to the square of 150.

 

[oswaler]

The maximum voltage in an RL circuit can be calculated using the equation Vmax = V0√(R^2 + (wL)^2), where V0 is the amplitude of the AC power source, R is the resistance of the resistor, w is the angular frequency (2πf), and L is the inductance of the inductor.

In a combined circuit with a resistor and inductor in series, the maximum voltage across the resistor and inductor will be the same, as they are in the same circuit. This can be seen by applying Kirchhoff's voltage law, which states that the sum of the voltages around a closed loop in a circuit must equal zero.

To find the maximum voltage for each component, you can use the individual voltage equations for a resistor and inductor in an AC circuit. The maximum voltage across a resistor is simply Vmax = V0, as the voltage across a resistor is in phase with the current. For an inductor, the maximum voltage is Vmax = wL * I0, where I0 is the amplitude of the current in the circuit.

I would also recommend familiarizing yourself with the concept of reactance in AC circuits, as it plays a crucial role in determining the maximum voltage in an RL circuit. Reactance is the opposition to the flow of AC current in an inductor, and it is represented by the term wL in the maximum voltage equation. As the frequency of the AC power source increases, the reactance of the inductor also increases, resulting in a higher maximum voltage across the inductor.

I hope this helps and good luck with your studies in AC circuits!