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).
Two inductor P and Q having inductance ration 1 : 2 are connected in p...
Answer should be v1/v2= 1/2