A circuit contains two elements, but it is not known if they or L, R or C. When

Question

A circuit contains two elements, but it is not known if they or L, R or C. When this circuit is connected to a 878 V 40.2 Hz A.C. source, the rms current is 6.87 A and leads the voltage by 36.6o. Find the two elements and their values. (For the one that is not there, the value is zero.)

Explanation / Answer

Z = sqrt[R^2 +(1/wC -wL)^2] I0 = 6.87 *sqrt2 = 9.716 A V = 878 V now, I = V/Z => sqrt[R^2 +(1/wC -wL)^2] = 90.37 => R^2 + (1/40.2C -40.2L)^2 = 8166.74     --->(1) also, tan (36.6) = (1/wC -wL)/R => 0.74 = (1/40.2C -40.2L)/R => 0.74 R = 0.025 C - 40.2 L     --->(2) w =sqrt(1/LC) => 1/LC = 1616.04     --->(3) solving the above three equations, we will get our result.

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