Final answer:
The value of the resistance in an LRC series circuit with given voltage amplitudes for inductor and capacitor can be found using the equation R + 310 + 200 = 250.
Step-by-step explanation:
In an LRC series circuit, the impedance (Z) is given by the formula:
Z = √(R^2 + (Xl - Xc)^2)
Where R is the resistance, Xl is the inductive reactance, and Xc is the capacitive reactance. In this case, the source voltage amplitude (v) is 250 V, the inductor voltage amplitude (Vl) is 310 V, and the capacitor voltage amplitude (Vc) is 200 V. Since the impedance is the sum of resistance, inductive reactance, and capacitive reactance, we can set up the following equations:
R + Xl + Xc = Z
R + vl + vc = v
Substituting the given values, we get:
R + 310 + 200 = 250
R + 510 = 250
R = 250 - 510
R = -260
The value of the resistance in the circuit is -260 ohms.