How much energy is stored in the 120 uf capacitor of a defibrillator if the potential across the plates is
4 x 10^3 V?
To determine the amount of energy stored in a capacitor, you can use the formula:
E = 0.5 * C * V^2
Where:
E is the energy stored in the capacitor
C is the capacitance
V is the potential difference (voltage) across the capacitor plates
In this case, you have a 120 µF (microfarad) capacitor with a potential difference of 4 x 10^3 V. Plugging these values into the formula, we get:
E = 0.5 * (120 x 10^-6 F) * (4 x 10^3 V)^2
First, we simplify the equation:
E = 0.5 * 120 µF * (4,000 V)^2
E = 0.5 * 120 * 10^-6 F * 16 x 10^6 V^2
Next, we use exponential arithmetic to calculate:
E = 0.5 * 120 * 10^-6 * 16 x 10^6 V^2
E = 0.5 * 120 * 16 x 10^6 * 10^-6 V^2
E = 0.5 * 1,920 x 10^6 * V^2
Finally, we simplify the equation and express the result in Joules (J):
E = 960 * 10^6 * V^2 J
Therefore, the energy stored in a 120 µF capacitor with a potential difference of 4 x 10^3 V is 960 x 10^6 times the square of the voltage (in joules).