Final answer:
To determine the expression of current in the circuit with applied voltage e(t) = 150sin(100πt), calculate the total impedance by combining the resistance and inductive reactance, and then divide the voltage by the impedance using Ohm's Law to find the current i(t).
Step-by-step explanation:
To find the expression of the current in the series circuit with an applied voltage e(t) = 150sin(100πt), we need to determine the total impedance in the circuit which includes both the resistance (R) and the inductive reactance (XL) due to the inductor (L). The resistance R is given as 10 ohms, and the inductance L is given as 0.318 henry.
The inductive reactance XL is calculated using the formula XL = ωL, where ω is the angular frequency of the voltage source. Since the voltage e(t) has a frequency of 50 Hz (as indicated by 100πt, where 100π is 2ω), ω is equal to 50π rad/s. Thus, the inductive reactance XL is XL = 50π × 0.318.
Once we have XL, we can determine the total impedance Z of the circuit using the formula Z = √(R2 + XL2). The expression for the current i(t) through the circuit can then be found by dividing the voltage e(t) by the total impedance Z using Ohm's Law, which gives us i(t) = e(t)/Z. The current i(t) will also have a sine waveform but possibly with a phase shift due to the presence of the inductor.