A 2200 μF capacitor is charged to a potential difference of 9 V and then allowed to discharge through a 100 kΩ resistor. Calculate the initial charge on the capacitor*1 point1.98 × 10^4 C1.98 × 10^-4 C1.98 x 10^2 C1.98 × 10^-2 C
Question
A 2200 μF capacitor is charged to a potential difference of 9 V and then allowed to discharge through a 100 kΩ resistor. Calculate the initial charge on the capacitor*1 point1.98 × 10^4 C1.98 × 10^-4 C1.98 x 10^2 C1.98 × 10^-2 C
Solution 1
The initial charge (Q) on a capacitor can be calculated using the formula:
Q = CV
where: C is the capacitance, which is 2200 μF or 2.2 mF (millifarads), and V is the potential difference, which is 9 V.
Substituting these values into the formula gives:
Q = 2.2 mF * 9 V = 19.8 mC (millicoulombs)
To convert millicoulombs to coulombs, we divide by 1000, so:
Q = 19.8 mC / 1000 = 0.0198 C
So, the initial charge on the capacitor is 0.0198 C, which is equivalent to 1.98 × 10^-2 C.
Solution 2
The initial charge (Q) on a capacitor can be calculated using the formula Q = CV, where C is the capacitance and V is the voltage.
Here, C = 2200 μF = 2200 x 10^-6 F (because 1μF = 10^-6 F) and V = 9 V.
So, Q = CV = 2200 x 10^-6 F x 9 V = 1.98 x 10^-2 C
So, the initial charge on the capacitor is 1.98 × 10^-2 C.
Solution 3
The initial charge (Q) on a capacitor can be calculated using the formula:
Q = CV
where: C is the capacitance, which is 2200 μF or 2.2 mF (since 1μF = 10^-3 mF) V is the potential difference, which is 9 V
Substituting the given values into the formula, we get:
Q = 2.2 mF * 9 V = 19.8 mC
However, the answer should be in Coulombs (C), not milliCoulombs (mC). Since 1mC = 10^-3 C, we convert the charge to Coulombs:
Q = 19.8 mC * 10^-3 = 0.0198 C
So, the initial charge on the capacitor is 0.0198 C. Looking at the options, this is closest to 1.98 × 10^-2 C.
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