Your Question:

10.51 a) Find the steady-state expression for the currents i_(s) and i_(i_(0)) in the circuit in Fig. P10.51 when v_(g)=400 cos 400 tV. b) Find the coefficient of coupling. c) Find the energy stored in the magnetically coupled coils at t=1.25 pims and t=2.5 pims d) Find the power delivered to the 375 Omega resistor. e) If the 375 Omega resistor is replaced by a variable resistor R_(L), what value of R_(L) will yield maximum average power transfer to R_(L) ? f) What is the maximum average power in (e)? g) Assume the 375 Omega resistor is replaced by a variable impedance Z_(L). What value of will result in maximum average power transfer to Z_(L) ? h) What is the

Step By Step Answers with Explanation

a) The steady-state expression for the currents i_(s) and i_(i_(0)) in the circuit in Fig. P10.51 when v_(g)=400 cos 400 tV can be found using the following steps:

1. Calculate the impedance of the secondary circuit, Z_(2):

Z_(eq) = Z_(1) + jωM * i_(i_(0)) / i_(s)

where Z_(1) is the impedance of the primary circuit, which is equal to R_(1) + jωL_(1) = 50 + j400π Ω.

b) The coefficient of coupling, k, is defined as the ratio of the mutual inductance, M, to the geometric mean of the self-inductances, L_(1) and L_(2):

k = M / √(L_(1) * L_(2)) = 0.7

P = i_(i_(0))^2 * R_(2)

e) The value of R_(L) that yields maximum average power transfer to R_(L) is equal to the magnitude of the equivalent impedance of the primary circuit, Z_(eq).

P_(max) = 1/2 * (v_(g)^2 / |Z_(eq)|^2)

Note: The above equations are based on the following assumptions:

• The impedance Z_(L) is linear.