A) Find the equivalent capacitance of the combination shown in the figure (Figur

Question

A) Find the equivalent capacitance of the combination shown in the figure (Figure 1) ? Express your answer using two significant figures in microF. (C=?)

B) Find the charge on each capacitor when a 100-V battery is connected across the combination.

Express your answers using two significant figures separated by commas in microC. (Q_1, Q_2, Q_3 = ?,?,?)

C) Find the voltage on each capacitor.

Express your answers using two significant figures separated by commas in Volts. (V_1, V_2, V_3 =?,?,?)

Explanation / Answer

Hi,

A) In this case we can see that the capacitors 2 and 3 are in parallel, so the equivalent capacitance of them is:

C = C2 + C3 = 0.01 uF + 0.02 uF = 0.03 uF

Besides, this new capacitor and the capacitor 1 are in series, therefore:

1/Ceq = 1/C + 1/C1 = 1/0.03 + 1/0.02 = 83.33 :::: Ceq = 1/83.33 = 0.012 uF

B and C) If a battery of 100 V is connected across, the combination the total charge is equal to:

Q = Ceq V = (0.012 uF)*(100 V) = 1.2*10-6 C

As the capacitor C (combination of 2 and 3) is in series with the capacitor 1 both of them have a charge equal to the total charge.

Q1 = Qc = Q = 1.2*10-6 C

Besides, the voltage of them (1 and C) can be found using the value of charge and its capacitances:

Vc = Q/C = 1.2*10-6C/ 0.03 uF = 40 V

V1 = Q/C1 = 1.2*106 C/ 0.02 uF = 60 V

To find the voltage of 2 and 3 we have to remember that they are in parallel and therefore its potentials are the equal to the total potential through them, so:

Vc = V2 = V3 = 40 V

The charges can be calculated using the voltage of each capacitor:

Q2 = V2*C2 = 40 V * 0.01 uF = 0.4*10-6 C

Q3 = V3*C3 = 40 V * 0.02 uF = 0.8*10-6 C

I hope it helps.

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