Answer :
The capacitance of the capacitor is 6 F when the 3 V battery is attached
We can use the equation Q = CV to solve this problem, where Q is the charge on the capacitor plates, C is the capacitance, and V is the voltage across the capacitor.
When a 6 V battery is attached to a 3 F capacitor, the charge on the capacitor plates is 18 C. Therefore:
Q = CV
18 C = 3 F x 6 V
Solving for C, we get:
C = Q/V = 18 C / 6 V = 3 F
Now, when the battery is replaced with a 3 V battery, the voltage across the capacitor is halved. Let's assume that the capacitance remains the same (we will verify this assumption later). Using the same equation, we can find the new charge on the capacitor plates:
Q = CV
Q = 3 F x 3 V
Q = 9 C
So, if the capacitance remained the same, the charge on the capacitor plates would be 9 C. However, we know that the charge on the capacitor plates should remain constant when we change the battery, since the capacitor is not discharged. Therefore, the capacitance must have changed to compensate for the halving of the voltage.
We can use the same equation as before to find the new capacitance:
C = Q/V = 18 C / 3 V = 6 F
Therefore, the capacitance of the capacitor is 6 F when the 3 V battery is attached.
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To find the new capacitance when replacing a 6 V battery with a 3 V battery while maintaining the same charge of 18 C, use the formula C = Q/V. The new capacitance would be 6 F.
When a 6 V battery is attached to a 3 F capacitor, the charge on the capacitor plates is 18 C. The relationship between charge (Q), capacitance (C), and voltage (V) is given by the formula Q = CV. Given this formula, if we replace the 6 V battery with a 3 V battery and want to find the capacitance that maintains the same 18 C of charge, we would rearrange the formula to solve for C, which gives us C = Q/V.
Using the 18 C of charge and the new voltage of 3 V, we can calculate the new capacitance as follows: C = 18 C / 3 V, which simplifies to C = 6 F. Therefore, when the battery is replaced with a 3 V battery, the capacitance of this capacitor is now 6 F.
