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kondor19780726 [428]
2 years ago
13

Capacitor C1 is initially charged to V1 and capacitor C2 is initially charged to V2. The capacitors are then connected to each o

ther, positive terminal to positive terminal and negative terminal to negative terminal.(a) If C1 = 24 μF with an initial voltage of 25 V, and capacitor C2 = 13 μF is charged to 11 V. What is the final voltage, in volts, across C1 ?
Physics
1 answer:
o-na [289]2 years ago
7 0

Answer:

<em>20.08 Volts</em>

Explanation:

<u>Parallel Connection of Capacitors</u>

The voltage across any two elements connected in parallel is the same. If the elements are capacitors, then each voltage is

\displaystyle V_1=\frac{Q_1}{C_1}

\displaystyle V_2=\frac{Q_2}{C_2}

They are both the same after connecting them, thus

\displaystyle \frac{Q_2}{C_2}=\frac{Q_1}{C_1}

Or, equivalently

\displaystyle Q_2=\frac{C_2Q_1}{C_1}

The total charge of both capacitors is

\displaystyle Q_t=Q_1\left(1+\frac{C_2}{C_1}\right)

We can compute the total charge by using the initial conditions where both capacitors were disconnected:

Q_t=V_{10}C_1+V_{20}C_2=25\cdot 24+13\cdot 11=743\ \mu C

Now we compute Q1 from the equation above

\displaystyle Q_1=\frac{Q_t}{\left(1+\frac{C_2}{C_1}\right)}=\frac{743}{\left(1+\frac{13}{24}\right)}=481.95\ \mu C

The final voltage of any of the capacitors is

\displaystyle V_1=V_2=\frac{481.95}{24}=20.08\ V

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