Question

What does the angular frequency of the emf have to be for the inductor and resistor have the same peak voltage (i.e. for R and XL to be the same)?

- At the angular frequency found in Q6, the phasor diagram (for a general time) is shown in the left most set of axes.
- Your answers to Q7-10 can be placed directly in the table below.

Answer 1

The peak voltage across a resistor and inductor in an AC circuit is the same when the resistor's resistance equals the inductor's reactance, which occurs at a specific angular frequency calculated by the formula ω = R / L.

Step-by-step explanation:

The question involves determining the angular frequency at which the peak voltage across both the resistor and inductor in an AC circuit is the same. This equality occurs when the resistor's resistance (R) equals the inductive reactance of the inductor (XL).

For a resistor-inductor (RL) circuit, the inductive reactance is given by XL = ωL, where ω is the angular frequency and L is the inductance. To have the same peak voltage across both components, we need R = XL, thus R = ωL. Solving for ω gives us ω = R / L. Substituting the given values, we can find the specific angular frequency required for the given circuit.

Answer 2

The angular frequency of the EMF needs to be 20/π rad/s for the inductor and resistor to have the same peak voltage.

Step-by-step explanation:

To find the angular frequency at which the resistor (R) and inductor (XL) have the same peak voltage, we need to compare their impedances. The impedance of a resistor is simply its resistance (R), while the impedance of an inductor is given by the formula XL = 2πfL, where f is the frequency and L is the inductance. At the resonance frequency, the impedance of the resistor and inductor are equal, so we can set R = XL and solve for the angular frequency (ω).

R = 2πfL

ω = 2πf

Setting R = XL:

R = 2πfL

200 = 2πf(2.5)

f = 20/π rad/s

So, the angular frequency of the EMF should be 20/pi rad/s for the inductor and resistor to have the same peak voltage.