The alternating voltage and current in an electric circuit are respectively given by E=100 100 t, I=5 100 t The reactance of the circuit will be

Step-by-step solution

The general equations of alternating voltage and current in an AC circuit are as follows E=E₀ t ...(i) I=I₀ t ...(ii) Given that, E=100 100 t ...(iii) I=5 100 t ...(iv) Comparing Eqs. (ii) and and (iv), we get, Peak value of current, I₀=5 ~A Comparing Eqs. (i) and (iii), we get Peak value of voltage, E₀=100 ~V Now, r.m.s. value of voltage is given by E_ rms = E₀ 2 = 100 2 ~V Similarly, r.m.s. value of current is given by I_ rms = I₀ 2 = 5 2 ~A Hence, reactance of the circuit is given by Z= E_ rms I_ rms = 100 2 5 2