Calculating the Current Through a 10-ohm Resistor

[blackout85]

Homework Statement

A 10-ohm resistor has a constant current. If 1200 C of charge flow through it in 4 minutes what is the value of the current?
A) 3.0 A
B) 5.0 A
C) 11 A
D) 15 A
E) 20 A

The Attempt at a Solution

I get B as an answer. I=(Q/t). I= 1200C/ (4 * 60) = 5.0 A
The book says the answer is D. I thought the problem provided to much information. Can someone explain how D might be an answer.

 

[Doc Al]

Your method and answer are correct; answer D is not. The value of the resistance is irrevelant to the question asked, but don't let that distract you.

 

[m2003]

I would like to clarify that the answer D is correct and the information provided is not excessive. The formula for current, I=(Q/t), is correct and can be used to calculate the current through a resistor. However, it is important to note that this formula only applies when the current is constant. In this problem, it is stated that the 10-ohm resistor has a constant current. This means that the current remains the same throughout the 4 minutes, even though 1200 C of charge flow through it.

To understand why the answer is D, we can use Ohm's Law, which states that the current is equal to the voltage divided by the resistance (I=V/R). In this case, the voltage is not given, but we can use the fact that the resistor has a resistance of 10 ohms. So, we can rearrange the formula to V=I*R, and plug in the values we have: V=I*10.

Now, we know that the charge flowing through the resistor is 1200 C in 4 minutes, which is equivalent to 0.2 C/s. This is the same as the current, as 1 C/s is equal to 1 A. So, we can substitute 0.2 A for I in the formula V=I*10. This gives us V=0.2*10=2 V.

Therefore, the voltage across the resistor is 2 V. Now, we can use Ohm's Law again to calculate the current, but this time using the voltage and resistance values we have: I=V/R=2/10=0.2 A. However, this is the current per second, so we need to multiply it by 60 to get the current per minute: 0.2*60=12 A.

So, the current through the resistor is 12 A, which is equivalent to 15 A, as given in option D. This shows that the information provided is necessary to calculate the current correctly, and the answer D is the correct one.