A 3.0- resistor and a 1.0- capacitor are connected in a single loop circuit with a seat of emf with . At 1.0 s after the connection is made, we have to find the rates at which (a) the charge on the capacitor is increasing, (b) the energy is being stored in the capacitor, (c) internal energy is appearing in the resistor, and (d) the energy is being delivered by the seat of emf.

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The variation of charge on a capacitor with time during the charging process is given by the equation

The rate of change of charge, , is the current . It is

The internal energy in the capacitor at time, t, will be

Therefore,

The rate at which internal energy is appearing in the resistor is

The rate at which the energy is being delivered by the seat of emf is

Data of our problem are:

In equations , , and , we will substitute the above values and use . We find

(a)

The rate of change of charge at is

(b)

The rate at which the energy is being stored in the capacitor is at is

(c)

The rate at which internal energy is appearing in the resistor at is

(d)

The rate at which the energy is being delivered by the seat of emf at is