Q. 305.0( 1 Vote )

# For an LCR circui

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=Vmsinωt  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.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses RELATED QUESTIONS :

(i) When an AC soPhysics - Board Papers

In the LCR circuiPhysics - Exemplar

Consider the LCR Physics - Exemplar

An electrical devPhysics - Exemplar

Explain why the rPhysics - Exemplar

Explain why the rPhysics - Exemplar

A coil of 0.01 hePhysics - Exemplar

In series LCR cirPhysics - Exemplar