Kirchhof\'s loop rule is a statement of the law of conservation of momentum. the

Question

Kirchhof's loop rule is a statement of the law of conservation of momentum. the law of conservation of charge. the law of conservation of energy the law of conservation of angular momentum. Newton's second law A resistor, an uncharged capacitor, a dc voltage source, and an open switch are all connected in series. The switch is closed at time t = 0 s. Which one of the following is a correct statement about this circuit? The charge on the capacitor after four time constants is about 98% maximum value. The charge on the capacitor after one time constant is 50% of its maximum value. The charge on the capacitor after one time constant is 1/e of its maximum value. The voltage on the capacitor after one time constant is 1/e of the maximum value The voltage on this capacitor after one time constant is 100% of its maximum value. A capacitor C is connected in series with a resistor R across a battery and an open switch. If a second capacitor of capacitance 2C is connected in parallel with the first one, the time constant of the new RC circuit will be the same as before. twice as large as before. three times a large as before. one-half as large as before one-fourth as large as before. A capacitor C is connected in series with a resistor R across a battery and an open switch. If a second capacitor of capacitance 2C is connected in series with the first one, the time constant of the new RC circuit will be the same as before. larger than before. smaller than before. variable.

Explanation / Answer

Solution:

67.

The principle of conservation of energy implies that

The directed sum of the electrical potential differences (voltage) around any closed network is zero,

or

The algebraic sum of the products of the resistances of the conductors and the currents in them in a closed loop is equal to the total emf available in that loop.

That issimilar to the energy conservtion law that we use in our classical physics(Mechnaics).

i.e;

Energy (initial) = Energy (final)

68.

As we know;

Q(t) = Qo [ 1 - e^-t/ ]

Putting t = 4

Q(t) = Qo (1- e^-4/)

=> Q(t) = Qo (0.9817)

That is approximately 98% of the initial charge(Qo)

69.

As we know;

Time constant = = RC

Here,

The final(after addind the second capacitor) capacitance value = 3C (2C + C // Capacitors in parallel adds up)

Hence

will become = 3RC

i.e

Three times

70.

Here

the equivalent capacitance would be (after adding the second capacitor);

C(eq.) = CxC / C+C

=> C(eq.) = C/2

Hence the new time constant is the half of the initial time constant because;

(new) = RC(eq.)

=> (new) = RC/2

Lesser than before!

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