A series RLC circuit consists of a 260 resistor, a 25 mH inductor, and a 18 F ca

Question

A series RLC circuit consists of a 260 resistor, a 25 mH inductor, and a 18 F capacitor.

1)What is the rms current if the emf is supplied by a standard 120 V , 60 Hz wall outlet?

The voltage-to-current ratio in the primary coil of a transformer can be though of as the transformer's effective resistance. A step-down transformer converts 120 V at the primary to 25 V at the secondary, which is connected to a load of resistance 6.0 .

2)What is the effective resistance of this transformer when connected to this load? (Hint: Resistance is defined as the ratio of two circuit quantities.)

Explanation / Answer

1) resistance is R = 260 ohm

inductive reactance is XL = 2*pi*f*L = 2*3.142*60*0.025 = 9.426 ohm

capacitive reactance is Xc = 1/(2*pi*f*C) = 1/(2*3.142*60*18*10^-6) = 147.34 ohm
impedence Z = Sqrt[(R^2+(XL-XC)^2]

Z = Sqrt[(260^2 + (9.426^2+147.34^2) = 299 ohm

rms current is Irms = V/Z = 120 /299 =0.4013 A

2) Power must be equal.

On the low voltage side, P = V^2/R = 25^2/6 = 104.16 W

On the high voltage side, P = IV -> 104.16 W -> I = 104.16/120 = 0.868 A

R = V/I = 120/0.868= 138.24 Ohms

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