A capacitor acquires 0.002 coulomb when 50 volts is applied. Its capacitance is
a. 0.4 microfarad
b. 4.0 microfarads
c. 40.0 microfarads
d. 400.0 microfarads
Well, well, well, it seems like we have a capacitor conundrum here! Let's tackle this volt-filled question with a splash of humor.
To find the capacitance, we can use the formula C = Q/V, where C is the capacitance in farads, Q is the charge in coulombs, and V is the voltage in volts. In this case, the charge acquired by the capacitor is 0.002 coulombs, and the voltage applied is 50 volts.
So, plugging in those values, we get C = 0.002 coulombs / 50 volts. Simplifying that, we find C = 0.00004 farads.
Hmmm, that answer isn't among the options. But have no fear, we just need to convert farads to microfarads. Since 1 microfarad is equal to 1 * 10^-6 farads, let's multiply our answer by 10^6 to convert it.
Calculating that, we get C = 0.00004 farads * 10^6 = 40 microfarads.
So, the capacitance of the capacitor is 40.0 microfarads, which just so happens to be option c. Voila!
To find the capacitance, we can use the formula:
C = Q/V
Where:
C is the capacitance
Q is the charge acquired by the capacitor
V is the voltage applied to the capacitor
Given:
Q = 0.002 coulomb
V = 50 volts
Plugging these values into the formula:
C = 0.002 coulomb / 50 volts
C = 0.00004 farad
Since the given options are in microfarads, we need to convert the result into microfarads.
1 farad is equal to 1,000,000 microfarads.
Therefore,
C = 0.00004 farad * 1,000,000 microfarads / 1 farad
C = 40 microfarads
Therefore, the correct answer is c. 40.0 microfarads.
To find the capacitance of the capacitor, we can use the formula:
C = Q / V
Where:
C is the capacitance in farads
Q is the amount of charge in coulombs
V is the voltage in volts
In this case, we are given that the capacitor acquires 0.002 coulombs of charge when 50 volts is applied. Let's substitute these values into the formula:
C = 0.002 C / 50 V
Now, we can simplify the equation:
C = 0.002 C / 50 V
C = 0.00004 F or 4.0 * 10^(-5) F
Since the units in the options are in microfarads (µF), we need to convert the capacitance from farads to microfarads by multiplying by 10^6:
C = 4.0 * 10^(-5) F * 10^6 = 40 µF
Therefore, the capacitance of the capacitor is 40.0 microfarads (c).