Answer :

Given:

Equation given :

(i)

Multiplying the equation by I,

Multiplying by (1/2) and substituting i=dq/dt

Hence, the simplified equation.

(ii)

Here, first term: means the rate of change of energy stored in the inductor.

Second term : represents the Joule’s Heating Loss.

Third Term: Represents rate of change of energy in Capacitor.

Fourth term: represents the energy due to driving force. It increases stored energy in inductor and capacitor.

(iii)

Conservation of Energy states that:

The sum of the individual energies across the individual components is equal to the total power of the circuit.

The equation in the form of a conservation of energy statement is

(iv)

Integrating the equation from 0 to T with resected to dt.

The integral of first term and third term would be zero as d/dt and dt gets cancelled. and V=V_{m}sinωt

LHS is positive as i, R and T are always positive, hence RHS is also positive.

Hence, phase difference between v and I must be acute for the cycle to be positive.

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