I wonder if the resonant frequency is 50hz
freson=1/2PI sqrtLC
solve for C
Power=mag (V*I) cosAnglebetween
RCL Circuits electricity!?
A 50V, 50Hz supply is connected to a series circuit consisting of a resistance, a 20mH inductor and a capacitor.
a) Find the value of the capacitance and the power dissipated in the circuit when:
(i) The current has a magnitude of 25A and leads the voltage by 45degrees.
(ii) The current has a magnitude of 25A and lags the voltage by 45degress.
(iii) The current and voltage are in phase.
b) If the frequency of the supply can be increased from 50Hz, using the value of the capacitance found in (i), find the frequency other than 50Hz when the current will have a magnitude of 25A.
3 answers
a1. Z(Ohms) = 50/25A[45o] = 2[-45o] = 2*Cos(-45) + j2*sin(-45) = 1.414 - j1.414.
Xl+Xc = -1.414, 6.28*50*0.020+Xc = -1.414, Xc = -7.69 Ohms.
C = 1/W*Xc = 1/(314.2*7.69) = 4.14*10^-4 Farads = 414 uF.
P = I^2*R = 25^2 * 1.414 = 884 Watts.
a2. Same procedure as a1.
a3. Z(Ohms) = E/I = 50/25A[0o] = 2[0o]. Xl+Xc = 0, Xc = -Xl = -WL = -314.2 * 0.020 = -6.28 Ohms.
C = 1/W*Xc = 1/(314.2*6.28) = 5.1*10^-4 Farads = 510 uF.
P = I^2*R = 25^2 * 2 = 1250 Watts.
Xl+Xc = -1.414, 6.28*50*0.020+Xc = -1.414, Xc = -7.69 Ohms.
C = 1/W*Xc = 1/(314.2*7.69) = 4.14*10^-4 Farads = 414 uF.
P = I^2*R = 25^2 * 1.414 = 884 Watts.
a2. Same procedure as a1.
a3. Z(Ohms) = E/I = 50/25A[0o] = 2[0o]. Xl+Xc = 0, Xc = -Xl = -WL = -314.2 * 0.020 = -6.28 Ohms.
C = 1/W*Xc = 1/(314.2*6.28) = 5.1*10^-4 Farads = 510 uF.
P = I^2*R = 25^2 * 2 = 1250 Watts.
P = I^2*R = 25^2 * 1.414 = 884 Watts.
1 answer