A series LCR circuit is connected across a source E of e.m.f. E=15 (50 t- 3 ) . The current from the supply is I=5 (50 t+ 6 ) . The impedance of the circuit and the phase difference between e.m.f. and current are, respectively, [all the quantities in the above two equations are in SI units.]

Step-by-step solution

Given the equations for e.m.f. and current: E = 15 (50 t - 3 ) I = 5 (50 t + 6 ) The peak voltage is E₀ = 15 V and the peak current is I₀ = 5 A. The impedance of the circuit is given by: Z = E₀ I₀ = 15 5 = 3 The phase of the e.m.f. is _E = 50 t - 3 and the phase of the current is _I = 50 t + 6 . The phase difference between the e.m.f. and the current is: = | _I - _E| = | (50 t + 6 ) - (50 t - 3 ) | = 6 + 3 = 6 + 2 6 = 3 6 = 2 radians. Thus, the impedance is 3 and the phase difference is ( 2 )^ c . Answer: 3 , ( 2 )