How does Kirchhoff's Loop Rule apply to an AC generator with a resistor?

[Pete_01]

Homework Statement

A resistor of resistance R is connected to an AC
generator with EMF(t)=(EMF_max)sin((w_d)t). (a) Write
Kirchhoff's Loop Rule for this circuit at a particular
instant of time. Is your result a differential equation?
(b) Find the current as a function of time. Now assume
R=50 Ohm and EMF_max = 30.0 V. (c) What is the amplitude
of the resulting alternating current if the frequency of
the EMF is 1.00 kHz?

Homework Equations

V_R = R dQ(t)/dt

The Attempt at a Solution

Ok, so the differential equation I came up with is:
V_G + V_R = 0
E_m sin(w_d t) = R dQ(t)/dt

assuming that's correct how do I find the current as a function of time? Replace dq/dt with i? And after that?

 

[Delta2]

And after that u get equation $$E_m sin(w_d t)=R I$$, hence $$I=\frac {E_m sin(w_d t)}{R}$$ and the amplitude of the ac current is $$\frac{E_m}{R}$$

Something else, usually we apply Kirchoff's Law with currents and voltages and not with charges Q. Therefore MAYBE the correct answer to a) is by having replace dq/dt with I from the start and therefore the equation isn't a differential equation.

 

[Pete_01]

Perfect, thank you!