Advertisements
Advertisements
Question
A circuit is set up by connecting inductance L = 100 mH, resistor R = 100 Ω and a capacitor of reactance 200 Ω in series. An alternating emf of \[150\sqrt{2}\] V, 500/π Hz is applies across this series combination. Calculate the power dissipated in the resistor.
Advertisements
Solution
Given the r.m.s value of emf in the circuit Ev = 150√2 V
The impedance of the LCR- circuit is given by
\[Z = \sqrt{R^2 + \left( X_L - X_C \right)^2}\]
\[ = \sqrt{R^2 + \left( 2\pi fL - 200 \right)^2}\]
\[ = \sqrt{{100}^2 + \left( 2\pi \times \frac{500}{\pi} \times 0 . 1 - 200 \right)^2}\]
\[ = 100\sqrt{2} \Omega\]
The r.m.s value of current Iv in the circuit is given by
\[I_v = \frac{E_v}{Z} = \frac{150\sqrt{2}}{100\sqrt{2}} = 1 . 5 A\]
Power dissipated in the resistor = EvIv = 318.2 W
APPEARS IN
RELATED QUESTIONS
A capacitor 'C', a variable resistor 'R' and a bulb 'B' are connected in series to the ac mains in circuit as shown. The bulb glows with some brightness. How will the glow of the bulb change if (i) a dielectric slab is introduced between the plates of the capacitor, keeping resistance R to be the same; (ii) the resistance R is increased keeping the same capacitance?
An electrical technician requires a capacitance of 2 µF in a circuit across a potential difference of 1 kV. A large number of 1 µF capacitors are available to him each of which can withstand a potential difference of not more than 400 V. Suggest a possible arrangement that requires the minimum number of capacitors.
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.
Find the charges on the four capacitors of capacitances 1 μF, 2 μF, 3 μF and 4 μF shown in the figure.
Three capacitors of capacitance `C_1 = 3muf` , `C_2 = 6muf` , `C_3 = 10muf` , are connected to a 10V battery as shown in figure 3 below :
Calculate :
(a) Equivalent capacitance.
(b) Electrostatic potential energy stored in the system
Three capacitors each of 4 µF are to be connected in such a way that the effective capacitance is 6µF. This can be done by connecting them:
The equivalent capacitance of the combination shown in the figure is ______.
Two charges q1 and q2 are placed at (0, 0, d) and (0, 0, – d) respectively. Find locus of points where the potential a zero.
A capacitor of capacity C1 is charged to the potential of V0. On disconnecting with the battery, it is connected with an uncharged capacitor of capacity C2 as shown in the adjoining figure. Find the ratio of energies before and after the connection of switch S.
Three capacitors of capacitances 2 pF, 3 pF and 4 pF are connected in parallel. What is the total capacitance of the combination?
