Question

What Voltage Is Required To Store 14.0mj Of Electrical Energy On A 6.0×10⁻⁹ F Capacitor?

A. 46 V
B. 9.5 V
C. 2.2×10³ V
D. 9.3×10⁻⁴ V
E. 4.8×10⁴ V

Answer 1

To determine the voltage needed to store 14.0 mJ on a 6.0×10⁻⁹ F capacitor, the formula E = 0.5 × C × V² is used. After plugging in the values and solving for V, the voltage is calculated to be 68.3 volts, which doesn't match any of the provided options exactly, but is closest to option A. 46 V.

Step-by-step explanation:

The question asks what voltage is required to store 14.0 mJ (millijoules) of electrical energy on a 6.0×10⁻⁹ F (farads) capacitor. To find the voltage, you can use the formula for the energy stored in a capacitor:

E = 0.5 × C × V²

Here, E is the energy in joules, C is the capacitance in farads, and V is the voltage in volts. Rearranging the formula to solve for V gives us:

V = √(2 × E / C)

Now, plug in the given values (remember to convert 14.0 mJ to joules by multiplying by 10⁻³):

V = √(2 × 14.0×10⁻³ J / 6.0×10⁻⁹ F)

V = √(2×14×10⁻³ / 6×10⁻⁹)

V = √(4.67×10⁳)

V = 68.3 volts

Therefore, the answer closest to our calculation that's offered in the options is A. 46 V; however, our calculation does not precisely match any of the provided options.