Question

A generator is connected to a resistor and a 0.042−H inductor in series. The rms voltage across the generator is 7.4 vi vvitertue generator frequency is set to 160 Hz, the rms voltage across the inductor is 1.5 V. Determine the resistance of the resistor in this circuit.

Answer 1

Step-by-step explanation:

To determine the resistance of the resistor in the circuit, we need to use the given information about the rms voltage across the generator and the rms voltage across the inductor.

First, let's find the impedance of the inductor using the formula:

Z = V / I

where Z is the impedance, V is the voltage across the inductor, and I is the current flowing through the inductor. Since we have the voltage across the inductor (1.5 V), we need to find the current flowing through it.

The current flowing through the inductor can be determined using the formula:

I = V / X

where X is the reactance of the inductor. The reactance of an inductor can be calculated using the formula:

X = 2πfL

where f is the frequency of the generator (160 Hz) and L is the inductance (0.042 H).

Let's calculate the reactance:

X = 2π(160)(0.042) = 16.9 Ω

Now we can find the current flowing through the inductor:

I = 1.5 V / 16.9 Ω ≈ 0.089 A

Next, let's calculate the impedance of the inductor:

Z = 1.5 V / 0.089 A ≈ 16.9 Ω

Since the generator, resistor, and inductor are connected in series, the total impedance of the circuit is the sum of the resistances. The impedance of the resistor is simply its resistance (R).

Therefore, the resistance of the resistor in this circuit is approximately 16.9 Ω.