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Two inductor P and Q having inductance ration 1 : 2 are connected in parallel in an electric circuit.The energy stored in the inductors P and Q are in the ratio
  • a)
    1 : 4
  • b)
    1 : 2
  • c)
    2 : 1
  • d)
    4 : 1
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Two inductor P and Q having inductance ration 1 : 2 are connected in p...
**Explanation:**

When two inductors are connected in parallel, the equivalent inductance (L_eq) is given by the reciprocal of the sum of the reciprocals of the individual inductances.

So, if P and Q are the individual inductances of the inductors, then the equivalent inductance (L_eq) is given by:

1/L_eq = 1/P + 1/Q

Given that the inductance ratio of P and Q is 1:2, we can assume that the inductance of P is x and the inductance of Q is 2x.

Substituting the values in the equation:

1/L_eq = 1/x + 1/2x

Simplifying the equation:

1/L_eq = (2 + 1)/2x

1/L_eq = 3/2x

Therefore, the equivalent inductance (L_eq) is given by:

L_eq = 2x/3

**Energy stored in an inductor:**

The energy stored in an inductor (W) is given by:

W = (1/2) * L * I^2

where L is the inductance and I is the current flowing through the inductor.

**Calculating the energy stored in inductor P:**

Let the current flowing through inductor P be I_P.

The energy stored in inductor P (W_P) is given by:

W_P = (1/2) * P * I_P^2

**Calculating the energy stored in inductor Q:**

Let the current flowing through inductor Q be I_Q.

The energy stored in inductor Q (W_Q) is given by:

W_Q = (1/2) * Q * I_Q^2

**Ratio of the energy stored:**

To find the ratio of the energy stored in inductors P and Q, we can substitute the values of P and Q in terms of x:

W_P = (1/2) * x * I_P^2

W_Q = (1/2) * 2x * I_Q^2

Simplifying the equations:

W_P = (1/2) * x * I_P^2

W_Q = x * I_Q^2

Dividing W_Q by W_P:

W_Q/W_P = (x * I_Q^2) / ((1/2) * x * I_P^2)

W_Q/W_P = (2 * I_Q^2) / I_P^2

W_Q/W_P = 2 * (I_Q / I_P)^2

**Relation between currents:**

Since the inductors P and Q are connected in parallel, the current through both inductors will be the same.

So, I_P = I_Q = I

Therefore, the ratio of the energy stored in inductors P and Q is:

W_Q/W_P = 2 * (I_Q / I_P)^2 = 2 * (I/I)^2 = 2 * 1^2 = 2

Hence, the energy stored in the inductors P and Q is in the ratio of 2:1, which corresponds to option (d).
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Community Answer
Two inductor P and Q having inductance ration 1 : 2 are connected in p...
Answer should be v1/v2= 1/2
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Two inductor P and Q having inductance ration 1 : 2 are connected in parallel in an electric circuit.The energy stored in the inductors P and Q are in the ratioa)1 : 4b)1 : 2c)2 : 1d)4 : 1Correct answer is option 'D'. Can you explain this answer?
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