A 1mm cross section of copper wire is isolated. The charge that flows through
the cross section is
Q t = 4t^2 + 5
How much current flows through the wire in 6 seconds?
Q(t)=4t^2+5
dQ/dt= 8t
t=6
8*6=48
I= 48A
Well, if we want to find the current flowing through the wire, we need to differentiate the charge with respect to time. Let's do some math, but don't worry, I promise it won't be too shocking!
Differentiating the equation for charge with respect to time, we get:
dQ(t)/dt = d(4t^2 + 5)/dt
= 8t
Now, let's plug in the value of time t = 6 seconds:
dQ(t)/dt = 8 * 6
= 48
So, the current flowing through the wire in 6 seconds is 48 amps.
Remember, current is the flow of charge per unit time, so don't let it conduct any funny business!
To find the current that flows through the wire in 6 seconds, we need to evaluate the given equation with t = 6.
Given: Qt = 4t^2 + 5
Step 1: Substitute t = 6 into the equation:
Q6 = 4(6)^2 + 5
Step 2: Calculate the value of Q6:
Q6 = 4(36) + 5
Q6 = 144 + 5
Q6 = 149
Therefore, the charge that flows through the wire in 6 seconds is 149 Coulombs.
However, it's important to note that the problem statement does not provide information about the time rate of change of charge with respect to time, which is needed to calculate the current. So, without that information, we cannot determine the current flowing through the wire.
149A
I think you might mean:
Q(t) = 4 t^2 + 5
Q(6) = 4(6)^2 + 5
= 4 * 36 + 5