A 4.00 µF capacitor is connected to a 18.0 V battery. How much energy is stored in the capacitor?
This should be a relatively easy problem yet, I can't get it. Isn't it just E=.5*C*V^2
E = (1/2) C V^2, yes
Remember that the "mu" symbol means "micro- or 10^-6
E = (1/2)*4*10^-6*(18)^2
= 6.48*10^-4 J
Keep three significant figures.
If your answer sheet or book does not agree with that answer, it is wrong.
awesome thanks, that's the correct answer. I was using the wrong conversion. :)
Well, well, well. Looks like we've got ourselves a little capacitor problem here. Let me grab my trusty calculator and put on my thinking hat.
Alrighty then! To calculate the energy stored in the capacitor, we can indeed use the formula E = 0.5 * C * V^2.
Plugging in the numbers you provided, we have:
C = 4.00 µF and V = 18.0 V
Now, before moving forward, let's convert that sneaky little µF to good ol' farads. 1 µF is equal to 0.000001 farads. So, our capacitance becomes:
C = 4.00 * 10^-6 F
Now, let's do some math magic.
E = 0.5 * 4.00 * 10^-6 F * (18.0 V)^2
Calculating that on my virtual slide rule gives us:
E = 0.001296 joules
Fun fact: 0.001296 joules is equivalent to the energy a clown expends while doing a single juggling trick.
So, your capacitor has stored approximately 0.001296 joules of energy. Don't spend it all in one place!
Yes, you are correct! The formula you mentioned, E = 0.5 * C * V^2, is indeed used to calculate the energy stored in a capacitor. Let's plug in the given values and solve the problem step by step.
Given:
C = 4.00 µF (microfarads)
V = 18.0 V (volts)
Step 1: Convert the capacitance from microfarads (µF) to farads (F).
To convert microfarads to farads, divide the given value by 1,000,000 (1 million).
C = 4.00 µF / 1,000,000 = 0.000004 F
Step 2: Substitute the values into the energy formula.
E = 0.5 * 0.000004 F * (18.0 V)^2
Step 3: Simplify the expression inside the parentheses.
E = 0.5 * 0.000004 F * (324 V^2)
Step 4: Calculate the square of the voltage.
V^2 = (18.0 V)^2 = 324 V^2
Step 5: Substitute the calculated value back into the equation.
E = 0.5 * 0.000004 F * 324 V^2
Step 6: Calculate the energy.
E = 0.5 * 0.000004 F * 324 V^2 = 0.000648 Joules
Therefore, the energy stored in the capacitor is 0.000648 Joules.