Lasers are used to try to produce controlled fusion reactions. These lasers require brief pulses of energy that are stored in large rooms filled with capacitors. One such room has a capacitance of 64 10-3 F charged to a potential difference of 7 kV.
(a) Given that W = 1/2CΔV2.
J, find the energy stored in the capacitors.
(b) The capacitors are discharged in 10 ns (1.0 10-8 s). What power is produced?
(c) If the capacitors are charged by a generator with a power capacity of 1.5 kW, how many seconds will be required to charge the capacitors?
(a) Your formuls should have been written
W = (1/2) C (ΔV)^2
All you have to do is use it. With ΔV = 7000 V and C = 64*10^-3 F, the answer will be in Joules.
(b) Power = Work/time
(c) (Generator power)* Time = Work
(Get the Work from part (a)
Solve for the time
Verygood
(a) The formula for energy stored in capacitors is given as:
W = 1/2 * C * ΔV^2
Where:
W = Energy stored in capacitors
C = Capacitance
ΔV = Potential difference
Given:
C = 64 * 10^-3 F (capacitance)
ΔV = 7 kV (potential difference)
Convert kV to V: 7 kV = 7 * 1000 V = 7000 V
Now, we can substitute the values into the formula:
W = 1/2 * (64 * 10^-3 F) * (7000 V)^2
W = 1/2 * 0.064 F * 49,000,000 V^2
W = 0.032 F * 49,000,000 V^2
W = 1,568,000 J
Therefore, the energy stored in the capacitors is 1,568,000 Joules (J).
(b) To calculate the power produced when the capacitors are discharged, we can use the formula:
Power (P) = Energy (W) / Time (t)
Given:
Energy stored in capacitors (W) = 1,568,000 J
Time (t) = 10 ns = 10 * 10^-9 s
Now substitute the values into the formula:
P = 1,568,000 J / (10 * 10^-9 s)
P = 1,568,000 J / 10^-8
P = 1.568 * 10^14 J/s
Therefore, the power produced when the capacitors are discharged is 1.568 * 10^14 Watts (W).
(c) To calculate the time required to charge the capacitors, we can use the formula:
Time (t) = Energy (W) / Power (P)
Given:
Energy stored in capacitors (W) = 1,568,000 J
Power capacity of the generator (P) = 1.5 kW = 1.5 * 10^3 W
Now substitute the values into the formula:
t = 1,568,000 J / (1.5 * 10^3 W)
t = 1,568,000 J / 1.5 * 10^3 W
t = 1.045 * 10^3 s
Therefore, it will take approximately 1.045 * 10^3 seconds to charge the capacitors.
(a) To find the energy stored in the capacitors, we can use the formula W = 1/2CΔV^2, where W is the energy stored, C is the capacitance, and ΔV is the potential difference.
Given:
Capacitance (C) = 64 * 10^-3 F
Potential difference (ΔV) = 7 kV (convert to volts by multiplying by 1000) = 7 * 10^3 V
Substituting these values into the formula, we get:
W = 1/2 * (64 * 10^-3) * (7 * 10^3)^2
Calculate the value:
W = 1/2 * 64 * 10^-3 * 49 * 10^6
W = 32 * 10^-3 * 49 * 10^6
W = 1568 * 10^3 J
W = 1.568 * 10^6 J
Therefore, the energy stored in the capacitors is 1.568 * 10^6 Joules.
(b) To find the power produced when the capacitors are discharged, we can use the formula P = W/t, where P is the power, W is the energy, and t is the time taken.
Given:
Energy (W) = 1.568 * 10^6 J
Time (t) = 10 ns (convert to seconds by dividing by 10^9) = 1.0 * 10^-8 s
Substituting these values into the formula, we get:
P = (1.568 * 10^6) / (1.0 * 10^-8)
Calculate the value:
P = 1.568 * 10^6 / 1.0 * 10^-8
P = 1.568 * 10^14 W
Therefore, the power produced when the capacitors are discharged is 1.568 * 10^14 Watts.
(c) To find the time required to charge the capacitors, we can use the formula t = W / P, where t is the time, W is the energy, and P is the power.
Given:
Energy (W) = 1.568 * 10^6 J
Power (P) = 1.5 kW (convert to Watts by multiplying by 1000) = 1.5 * 10^3 W
Substituting these values into the formula, we get:
t = (1.568 * 10^6) / (1.5 * 10^3)
Calculate the value:
t = 1.568 * 10^6 / 1.5 * 10^3
t = 1.045 * 10^3 s
Therefore, it will take approximately 1.045 * 10^3 seconds to charge the capacitors.