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 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).
Deduce an expression for equivalent capacitance C when three capacitors C1, C2 and C3 connected in parallel.
The following figure shows two capacitors connected in series and joined to a battery. The graph shows the variation in potential as one moves from left to right on the branch containing the capacitors.
Each plate of a parallel plate capacitor has a charge q on it. The capacitor is now connected to a batter. Now,
(a) the facing surfaces of the capacitor have equal and opposite charges
(b) the two plates of the capacitor have equal and opposite charges
(c) the battery supplies equal and opposite charges to the two plates
(d) the outer surfaces of the plates have equal charges
The plates of a capacitor are 2⋅00 cm apart. An electron-proton pair is released somewhere in the gap between the plates and it is found that the proton reaches the negative plate at the same time as the electron reaches the positive plate. At what distance from the negative plate was the pair released?
A parallel-plate capacitor having plate area 20 cm2 and separation between the plates 1⋅00 mm is connected to a battery of 12⋅0 V. The plates are pulled apart to increase the separation to 2⋅0 mm. (a) Calculate the charge flown through the circuit during the process. (b) How much energy is absorbed by the battery during the process? (c) Calculate the stored energy in the electric field before and after the process. (d) Using the expression for the force between the plates, find the work done by the person pulling the plates apart. (e) Show and justify that no heat is produced during this transfer of charge as the separation is increased.
An ac circuit consists of a series combination of circuit elements X and Y. The current is ahead of the voltage in phase by `pi/4`. If element X is a pure resistor of 100 Ω,
(a) name the circuit element Y.
(b) calculate the rms value of current, if rms of voltage is 141 V.
(c) what will happen if the ac source is replaced by a dc source
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)
