Maximum current IN the resistor

In summary, a 1.89 nF capacitor with an initial charge of 5.26 mC is discharged through a 1.34 kW resistor. The maximum current in the resistor can be found using the equation I(t) = -(Q/RC)*e^(-t/RC). Kirchoff's current law states that the magnitude of the current will be the same for both the capacitor and resistor in series. The maximum current value will be the initial value and the current coming out of the capacitor must be equal to the current going into the resistor.
  • #1
glid02
54
0
Here's what I know:
A 1.89 nF capacitor with an initial charge of 5.26 mC is discharged through a 1.34 kW resistor.

I'm supposed to find the maximum current in the resistor.

I know the maximum current through the resistor is -2.077 A from the equation I(t) = -(Q/RC)*e^(-t/RC) and I know how to find the terminal voltage - E - Ir, but I'm at a loss on how to find the maximum current in the resistor. Any help would be awesome.

Thanks a lot.
 
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  • #2
The maximum current is right in front of your eyes!

You either solved or were given the equation that I(t) = -(Q/RC)*e^(-t/RC) for the capacitor. Think about how this solution will look qualitatively - that is, graph it. I didn't plug the numbers into verify, but it looks like you figured the capacitors max current. What does Kirchoff's current law tell you (you'll have to figure out the passive sign convention for this i.e. what way the cap is oriented)?
 
  • #3
When t = 0 it is the highest (or lowest since it's negative) because e^0=1 so it's just -Q/RC

As t approaches infinity e^(-t/RC) will equal 0, so the extremes will be 0 and -Q/RC, right?

Is there a difference between that current and the current that's actually in the resistor?

Thanks.
 
  • #4
Right, the max current value will be the initial value.

If the capacitor and resistor are in series, which they would have to be for that equation, then the magnitude of the current is the same because Kirchoff's current law will tell you that the current coming out of the cap must be the current into the resistor.
 
  • #5
Great.

Yeah, it was the magnitude not the actual current.

Thanks.
 

1. What is the maximum current that can flow through a resistor?

The maximum current that can flow through a resistor is determined by the resistance value of the resistor and the voltage applied across it. It can be calculated using Ohm's Law (I=V/R) where I is the current in amps, V is the voltage in volts, and R is the resistance in ohms.

2. How does the maximum current affect the performance of a resistor?

The maximum current rating of a resistor is an important factor in its performance. If the current exceeds the maximum rating, the resistor may overheat and potentially fail. It is important to choose a resistor with a maximum current rating that can handle the expected current in a circuit.

3. Can the maximum current in a resistor change with temperature?

Yes, the maximum current rating of a resistor can change with temperature. This is because the resistance of a material can vary with temperature, and a higher temperature can increase the resistance of a resistor, resulting in a lower maximum current rating.

4. How can I determine the maximum current rating of a resistor?

The maximum current rating of a resistor is typically provided by the manufacturer. It can also be calculated by dividing the maximum power rating of the resistor by its maximum voltage rating. For example, a resistor with a maximum power rating of 1 watt and a maximum voltage rating of 10 volts would have a maximum current rating of 0.1 amps (1 watt / 10 volts = 0.1 amps).

5. Is the maximum current rating the only factor to consider when choosing a resistor?

No, the maximum current rating is not the only factor to consider when choosing a resistor. Other important factors include the resistance value, tolerance, and power rating. It is important to choose a resistor that can handle the expected current, but also meets the other requirements of the circuit.

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