two capacitors of capacitance of 6 micro farad and 12 micro farad are connected in series with a battery. the voltage across the 6 micro farad capacitance is 2 V.Compute the total battery voltage.
To determine the total battery voltage, we need to apply the principles of capacitance in series. When capacitors are connected in series, the total capacitance (C_total) is given by the reciprocal of the sum of the reciprocals of the individual capacitances (C1 and C2):
1/C_total = 1/C1 + 1/C2
Given that the capacitance of C1 is 6 μF and the capacitance of C2 is 12 μF, we can substitute these values into the equation:
1/C_total = 1/6μF + 1/12μF
To simplify the equation, we need to find the common denominator of the fraction. In this case, the common denominator is 12:
1/C_total = 2/12μF + 1/12μF
Combining the fractions:
1/C_total = 3/12μF
Simplifying further:
1/C_total = 1/4μF
Now, we can take the reciprocal of both sides to find the total capacitance:
C_total = 4μF
Next, we need to use the formula for the voltage across a capacitor when it is connected to a battery:
V = Q/C
Where V is the voltage, Q is the charge stored on the capacitor, and C is the capacitance.
Given that the voltage across the 6 μF capacitor is 2 V and the capacitance is 6 μF, we can rearrange the formula to find the charge (Q) on the capacitor:
Q = V * C
Q = 2 V * 6 μF
Q = 12 μC
Since the sum of the charges on the capacitors in series is equal to the charge on the battery, the total charge on the battery (Q_total) is the same as the charge on the 6 μF capacitor:
Q_total = 12 μC
Finally, we can find the total battery voltage (V_total) using the formula:
V_total = Q_total / C_total
V_total = 12 μC / 4 μF
V_total = 3 V
Therefore, the total battery voltage is 3 V.