Answer:
56.04 ohms
Step-by-step explanation:
The voltage across the inductor VL = IXL
I is the total current flowing in the circuit and XL is the inductive reactance.
First we need to get the current flowing in the circuit.
From the expression above;
I = VL/XL
Since XL = 2πfL
I = VL/ 2πfL
Given VL = 2.8V, frequancy f = 100Hz and inductance L = 0.049-H
I = 2.8/2π*100*0.049
I = 2.8/30.79
I = 0.091A
Also;
Vrms = VL + VR
VR is the voltage across the resistor.
VR = Vrms - VL
VR = 7.9 - 2.8
VR = 5.1V
Then we can calculate the resistance of the resistor
According to ohms law VR = IR
Since the inductance and resistance ar connected in series, the same current will flow through them.
R = VR/I
R = 5.1/0.091
R = 56.04 ohms
Hence the resistance of the resistor in this circuit is 56.04 ohms