An AC generator delivers an alternating current
I(t) = (3.4 A) sin[(140π rad/s)t]
to a single resistor in series with the generator.
(a) What is the rms value of the current in the circuit?
(b) If the resistor has a resistance of 240.0 Ω, what is the rms value of the source emf?
(c) What is the maximum value of the source emf?
(d) Write a function that describes the source emf as a function of time. (Use the following as necessary: t. Do not use other variables, substitute numeric values. Assume that e m f is in volts and t is in seconds. Do not include units in your answer.)
This is pretty simple stuff. I will be happy to critique your work.
I can't. Need to know the formula first. Do you know the formulas?
To answer these questions, we'll need to understand the concepts of RMS value, resistance, and maximum value of source emf. Let's go step by step.
(a) The RMS value of an alternating current is given by the formula:
Irms = Imax / √2
where Imax is the maximum value of the current. In this case, the maximum value of the current is 3.4 A. So, we can calculate the RMS value as follows:
Irms = 3.4 A / √2
≈ 2.405 A
So, the RMS value of the current in the circuit is approximately 2.405 A.
(b) The relationship between current (I), resistance (R), and emf (E) is given by Ohm's law:
I = E / R
In this case, we have the current (2.405 A) and resistance (240.0 Ω). Rearranging the formula, we can solve for the emf (E):
E = I * R
= 2.405 A * 240.0 Ω
= 577.2 V
So, the RMS value of the source emf (voltage) is 577.2 V.
(c) The maximum value of an alternating current or emf can be found by taking the peak value of the sinusoidal function. In this case, the function describing the current is:
I(t) = (3.4 A) sin[(140π rad/s)t]
We can see that the amplitude of the sine function is 3.4 A. So, the maximum value of the source emf is also 3.4 A.
(d) The function describing the source emf as a function of time is provided in the question:
E(t) = (3.4 V) sin[(140π rad/s)t]
The given function describes the emf in terms of time (t) using the sine function.