Solving for RMS current of a resistor, help?

In summary, when a resistor is connected across an AC power supply with 120 V rms, the current is given by I=(1.35A)cos(300t). To find the RMS current, we use the formula IRMS=Imax/√2 and read the maximum value from the coefficient, which is 1.35 A. Therefore, the RMS current is 0.955 A.
  • #1
clamatoman
24
0

Homework Statement


A resistor connected across an AC power supply has a current given by I=(1.35A)cos(300t) when connected to a power supply with emf 120 V rms.
Find the RMS current.

Homework Equations


IRMS=Imax/√2

The Attempt at a Solution


IRMS=Imax/√2
IRMS=0.477 A
INCORRECT
Not exactly sure what to do? I am not given any other data besides what i have written above. I do not have the Power, or the Resistance, and in fact will have to solve for those in part B. and C. of this problem. I know I am missing something here, and i have re-read the chapter in my textbook but it is not helping.
 
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  • #2
How did you establish the value of ##I_{max}## that you used?
 
  • #3
gneill said:
How did you establish the value of ##I_{max}## that you used?
I used the value of "I=(1.35A)cos(300t)" they gave as Imax.
 
  • #4
clamatoman said:
I used the value of "I=(1.35A)cos(300t)" they gave as Imax.
Okay, but that's not a value. What value (single number) did you use?
 
  • #5
gneill said:
Okay, but that's not a value. What value (single number) did you use?
I used (1.35A)cos(300t) = 0.675
I think what I am missing is what the "t" component means?
 
  • #6
clamatoman said:
I used (1.35A)cos(300t) = 0.675
That is incorrect for a couple of reasons. First, the expression cos(300t) is a function of time t. Second, the "300" in the expression would have units of radians per second, not degrees per second.

Read the maximum value from the coefficient: 1.35 A. The cosine function makes the current vary between the bounds -1.35 A and +1.35 A over time.
 
  • #7
gneill said:
That is incorrect for a couple of reasons. First, the expression cos(300t) is a function of time t. Second, the "300" in the expression would have units of radians per second, not degrees per second.

Read the maximum value from the coefficient: 1.35 A. The cosine function makes the current vary between the bounds -1.35 A and +1.35 A over time.
Ahh Okay.
So.
Imax=1.35 A
IRMS=1.35/√2=.955 A
Excellent, thank you.
 

Related to Solving for RMS current of a resistor, help?

1. What is RMS current and why is it important?

RMS (Root Mean Square) current is a measure of the average current flowing through a circuit over time. It takes into account the varying amplitudes of the current and provides a more accurate representation of the actual current. It is important because it is used to calculate power dissipation and to determine the maximum current a circuit can handle without overheating.

2. How do I calculate the RMS current of a resistor?

To calculate the RMS current of a resistor, you can use the formula IRMS = Ipeak / √2, where Ipeak is the peak current. Alternatively, you can use the formula IRMS = VRMS / R, where VRMS is the RMS voltage across the resistor and R is the resistance value.

3. Can I use a multimeter to measure the RMS current of a resistor?

No, a multimeter can only measure the average (DC) current of a circuit. To measure the RMS current, you will need a special meter called an RMS meter or an oscilloscope.

4. Is the RMS current the same as the peak current?

No, the RMS current and peak current are two different values. The peak current is the maximum value of the current, while the RMS current is the average value over time. The RMS current is always lower than the peak current.

5. How does the RMS current affect the power dissipation of a resistor?

The power dissipation of a resistor is directly proportional to the RMS current. This means that as the RMS current increases, the power dissipation also increases. Therefore, it is important to calculate and consider the RMS current when designing a circuit to ensure the resistor can handle the power dissipation without overheating.

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