Calculating Voltage Across Capacitors | Series & Parallel Connections

[rave7]

A 2.41microF and a 7.38microF capacitor are connected in series across a 30.0-V battery. A 10.3microF capacitor is then connected in parallel across the 2.41-microF capacitor. Determine the voltage across the 10.3-F capacitor.

How do i approach this question. do i start by finding the total energy produced by the capacitors? since E=1/2 CV^2 .

 

[rave7]

oops. sorry for posting this question here. didnt know that there's another section for posting questions. apologies.

 

[astrokreng]

I would approach this question by first understanding the basic principles and equations governing capacitors in series and parallel connections. In series connections, the capacitors share the same charge, while in parallel connections, the capacitors have the same voltage across them.

To determine the voltage across the 10.3microF capacitor, we can use the equation for capacitors in parallel: C_eq = C1 + C2, where C_eq is the equivalent capacitance of the two capacitors in parallel. In this case, C1 is the 2.41microF capacitor and C2 is the 10.3microF capacitor, so C_eq = 2.41microF + 10.3microF = 12.71microF.

Next, we can use the equation for the voltage across capacitors in a parallel connection, V = Q/C, where V is the voltage, Q is the charge, and C is the capacitance. Since the voltage is the same across all capacitors in parallel, we can set V_eq (the voltage across the equivalent capacitor) equal to V1 (the voltage across the 2.41microF capacitor) and solve for Q_eq (the charge on the equivalent capacitor).

V_eq = V1 = Q_eq/C_eq
30.0V = Q_eq/12.71microF
Q_eq = 382.8microC

Now, we can use the equation for the voltage across capacitors in a series connection to find the voltage across the 10.3microF capacitor. V = Q/C, where V is the voltage, Q is the charge, and C is the capacitance. In this case, the charge on the 10.3microF capacitor is the same as the charge on the equivalent capacitor, Q_eq.

V_10.3microF = Q_eq/C_10.3microF
V_10.3microF = 382.8microC/10.3microF
V_10.3microF = 37.2V

Therefore, the voltage across the 10.3microF capacitor is 37.2V.