Advertisements
Advertisements
Question
When an AC source is connected to an ideal capacitor, show that the average power supplied by the source over a complete cycle is zero
Advertisements
Solution
The instantaneous power supplied to the capacitor is
P = im cos(ωt)vm sin(ωt)
P = imvm cos(ωt)sin(ωt)
`P=(i_mv_m)/2sin(2omegat)`
Therefore, the average power is
`(:P:) = (:(i_mv_m)/2sin(2omegat):)=(i_mv_m)/2(:sin(2omegat):)`
Now, the average of sin(2ωt) over the cycle is zero.
∴ ⟨P⟩ = 0
APPEARS IN
RELATED QUESTIONS
A capacitor of capacitance ‘C’ is charged to ‘V’ volts by a battery. After some time the battery is disconnected and the distance between the plates is doubled. Now a slab of dielectric constant, 1 < k < 2, is introduced to fill the space between the plates. How will the following be affected? (a) The electric field between the plates of the capacitor Justify your answer by writing the necessary expressions.
A parallel plate capacitor of capacitance C is charged to a potential V. It is then connected to another uncharged capacitor having the same capacitance. Find out the ratio of the energy stored in the combined system to that stored initially in the single capacitor.
Three capacitors of capacitances 6 µF each are available. The minimum and maximum capacitances, which may be obtained are
Convince yourself that parts (a), (b) and (c) figure are identical. Find the capacitance between the points A and B of the assembly.
Find the equivalent capacitances of the combinations shown in figure between the indicated points.
A sphercial capacitor is made of two conducting spherical shells of radii a and b. The space between the shells is filled with a dielectric of dielectric constant K up to a radius c as shown in figure . Calculate the capacitance.
Figure shows two parallel plate capacitors with fixed plates and connected to two batteries. The separation between the plates is the same for the two capacitors. The plates are rectangular in shape with width b and lengths l1 and l2. The left half of the dielectric slab has a dielectric constant K1 and the right half K2. Neglecting any friction, find the ration of the emf of the left battery to that of the right battery for which the dielectric slab may remain in equilibrium.
Calculate the resultant capacitances for each of the following combinations of capacitors.
When air is replaced by a dielectric medium of constant K, the maximum force of attraction between two charges separated by a distance ______.
Two identical capacitors are connected as shown and have an initial charge of Q0. The separation between the plates of each capacitor is d0. Suddenly the left plate of the upper capacitor and right plate of the lower capacitor start moving with speed v towards the left while the other plate of each capacitor remains fixed. `("given" (Q_0V)/(2d_0) = 10 A)`. The value of current in the circuit is ______ A.
