Two capacitors of capacitance 10 micro Farad and 12 micro Farad are connected in series with a battery. The voltage across the 12 micro Farad is 10 volts. Compute the total battery voltage.
The same charge is on each capacitor, so the voltage=10(1+10/12)
V=qC on each capacitor
When capacitors are connected in series, the charges on the plates are the same.
The formula for capacitors connected in series is:
1/C_total = 1/C1 + 1/C2
Let's calculate the total capacitance first:
1/C_total = 1/C1 + 1/C2
1/C_total = 1/10 µF + 1/12 µF
To add the fractions, we need a common denominator:
1/C_total = (12/12) * (1/10 µF) + (10/10) * (1/12 µF)
1/C_total = 12/120 µF + 10/120 µF
1/C_total = 22/120 µF
C_total = 120/22 µF
Now, we can use the formula for the total battery voltage in a series circuit:
V_total = V1 + V2
V_total = 10 V + V2
We know that the voltage across the 12 µF capacitor (V2) is 10 V, so:
V_total = 10 V + 10 V
V_total = 20 V
Therefore, the total battery voltage is 20 volts.
To compute the total battery voltage, you need to use the concept of applied voltage across capacitors in series. In a series connection, the same current flows through each capacitor, but the voltage across each capacitor can be different.
Here's how you can calculate the total battery voltage in this case:
1. First, calculate the charge on each capacitor.
The charge on a capacitor is given by the equation Q = CV, where Q is the charge, C is the capacitance, and V is the voltage across the capacitor.
For the 12 micro Farad capacitor:
Q1 = (12 micro Farad) * (10 volts) = 120 microCoulombs
2. Next, apply the principle of conservation of charge. Since the capacitors are connected in series, the same charge flows through each of them.
So, the charge on the 10 micro Farad capacitor (Q2) will also be equal to 120 microCoulombs.
3. Now, calculate the voltage across the 10 micro Farad capacitor.
Using the formula Q = CV, rearrange the formula to solve for V:
V2 = Q2 / C2
=> V2 = (120 microCoulombs) / (10 micro Farad)
=> V2 = 12 volts
Therefore, the voltage across the 10 micro Farad capacitor is 12 volts.
4. Finally, calculate the total battery voltage by adding up the individual voltages across the capacitors.
Total battery voltage = Voltage across the 12 micro Farad capacitor + Voltage across the 10 micro Farad capacitor
Total battery voltage = 10 volts + 12 volts
Total battery voltage = 22 volts
Hence, the total battery voltage is 22 volts.