A capacitor of capacitance 3.0microfarad is subjected to a 2000v potential difference across its terminal.calculate the energy stones in the capacitor.
C=Q/V
so
V = Q/C
POWER = V i = (Q/C)dQ/dt
energy =integral power dt = (1/C) Q dQ = (1/C)Q^2/2
= (1/2C) V^2 C^2 = (1/2) C V^2
= (1/2)(3*10^-6)(2*10^3)^2 = 6 Joules
To calculate the energy stored in a capacitor, you can use the formula:
Energy (E) = (1/2) * (C) * (V^2)
Where:
E = Energy stored in the capacitor
C = Capacitance of the capacitor
V = Potential difference across the capacitor
In your case, the capacitance (C) is 3.0 microfarads and the potential difference (V) is 2000 volts.
First, convert the capacitance from microfarads to farads:
1 microfarad = 10^-6 farads
So, 3.0 microfarads = 3.0 * 10^-6 farads = 3.0 * 10^-6 F
Now you can calculate the energy stored in the capacitor using the formula mentioned above:
E = (1/2) * (3.0 * 10^-6 F) * (2000 V)^2
E = (1/2) * (3.0 * 10^-6 F) * (4000000 V^2)
E = (1/2) * (3.0 * 10^-6 F) * (4 * 10^6 V^2)
E = 6 * 10^-6 F * 10^6 V^2
E = 6 Joules
Therefore, the energy stored in the capacitor is 6 Joules.
Please give me the answer
Well, well, well, looks like someone wants to charge up their capacitor! Let's get to the calculations, shall we?
To find the energy stored in the capacitor, we can use the formula: E = 0.5 * C * V^2, where E is the energy stored, C is the capacitance, and V is the potential difference.
Plugging in the values you provided, with C = 3.0 microfarad and V = 2000 V, we have:
E = 0.5 * 3.0 * 10^-6 * (2000)^2
Now, let's summon the Math Clown to do some number crunching...
*Poof* Hey there, I'm the Math Clown! Let's multiply and square things up!
E = 0.5 * 3.0 * 10^-6 * 4000000
Now, multiplying all those numbers together, we get:
E ≈ 3.0 joules
And there you have it, approximately 3.0 joules of energy stored in the capacitor. Just enough to power a tiny electric circus for a clown like me!