Advertisements
Advertisements
Question
Figure 4 below shows a capacitor C, an inductor L and a resistor R, connected in series
to an a.c. supply of 220 V
Calculate:
1) The resonant frequency of the given CLR circuit.
2) Current flowing through·the circuit.
3) Average power consumed by the circuit.
Advertisements
Solution
`E_"rms" = 220 V`
`C = 25 muF`
`L = (4/pi^2)H`
R = 100 Ω
1) Resonant Frequency
`f_r = 1/(2pisqrt(LC))`
`= 1/(2xx 3.14 xx sqrt(4/pi^2 xx 25 xx 10^(-6)))`
`= 1/(2xx3.14 xx 2/3.14 xx 5 xx 10^(-3)) `
= 50 Hz
2) Inpedance (Z) = `sqrt(R^2 + (X_L - X_C)^2)`
`X_L = 127.3 Ω, X_C = 127.3 Ω`
Z = `sqrt(100^2 + (127.3 - 127.3)^2 )`
`Z = sqrt(100^2)`
Z = 100 Ω
`I_"rms" = E_"rms"/2`
`= 220/100`
`I_"rms" = 2.2 A`
3) Average power consumed by the circuit
Power = `E_"rms" xx I_"rms" xx R/sqrt(R^2 + (Lomega - 1/(Comega)))`
z = R
∴ Power = `E_"rms" xx I_"rms"`
Power = 484 watt
APPEARS IN
RELATED QUESTIONS
A cylindrical capacitor has two co-axial cylinders of length 15 cm and radii 1.5 cm and 1.4 cm. The outer cylinder is earthed and the inner cylinder is given a charge of 3.5 µC. Determine the capacitance of the system and the potential of the inner cylinder. Neglect end effects (i.e., bending of field lines at the ends).
The plates of a parallel-plate capacitor are given equal positive charges. What will be the potential difference between the plates? What will be the charges on the facing surfaces and on the outer surfaces?
A parallel-plate capacitor has plates of unequal area. The larger plate is connected to the positive terminal of the battery and the smaller plate to its negative terminal. Let Q, and Q be the charges appearing on the positive and negative plates respectively.
A parallel-plate capacitor is connected to a battery. A metal sheet of negligible thickness is placed between the plates. The sheet remains parallel to the plates of the capacitor.
Two parallel plate capacitors X and Y, have the same area of plates and same separation between plates. X has air and Y with dielectric of constant 2, between its plates. They are connected in series to a battery of 12 V. The ratio of electrostatic energy stored in X and Y is ______.
The total charge on the system of capacitors C1 = 1 µF, C2 = 2 µF, C3 = 4 µF and C4 = 3 µF connected in parallel is ______. (Assume a battery of 20 V is connected to the combination)
The equivalent capacitance of the combination shown is:
The potential difference that must be applied across the series and parallel combination of 4 identical capacitors such that the energy stored in them becomes the same. The ratio of potential difference in series to parallel combination is ______.
Compared with the individual capacitors in a series combination, how large is the equivalent capacitance?
Which relation gives the charge on one capacitor in a parallel combination when the common voltage is \[V\]?
