In the AC circuit shown, x is the reading of the voltmeter in volts and y is the reading of the ammeter in amperes. The source is 90 V, 60 Hz; R = 45 Ω, capacitive reactance X꜀ = 4 Ω and inductive reactance Xₗ = 4 Ω. Find x + y. [See Image.]
Physics · Mixed Chapter
JEE Mains

Question

In the AC circuit shown, x is the reading of the voltmeter in volts and y is the reading of the ammeter in amperes. The source is 90 V, 60 Hz; R = 45 Ω, capacitive reactance X꜀ = 4 Ω and inductive reactance Xₗ = 4 Ω. Find x + y. [See Image.]

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1 — From the original circuit diagram: R = 45 Ω, Xₗ = 4 Ω and X꜀ = 4 Ω. The source voltage is 90 V (rms). The voltmeter spans the series L–C section; the ammeter is in series with the source. Step 2 — Net reactance is X = Xₗ − X꜀ = 4 − 4 = 0 Ω. Hence Z = √[R² + X²] = 45 Ω. Step 3 — The ammeter indicates rms current y = V/Z = 90/45 = 2 A. Step 4 — In the L–C section the phasor voltages have opposite signs: Vₗ = IXₗ = 8 V and V꜀ = IX꜀ = 8 V. The voltmeter reads their phasor difference x = |V…