1. Students run their experiment by charging a capacitor. The voltage across the

Question

1. Students run their experiment by charging a capacitor. The voltage across the capacitor was increasing with time. In data analysis, they used computer and found a good fit for V(t) with the theoretical function for charging a capacitor:

The result of the computer fit gave them the following numbers:

A = 4.4; B = 0.0038; and C = 0.056

2. A capacitor is charged and the potential difference between its electrodes is equal to V0. The initial energy stored in this capacitor is U0. Next, the capacitor was partially discharged and the potential difference between the electrodes V was reduced to one half of the initial value V0. What was the change in electrical energy stored in the capacitor?

U/U0 = ?

3. A capacitor with capacitance C is completely charged using an external voltage V. The energy stored in this capacitor is equal to U1 = CV2/2.

(a) What would be the energy U2 stored in twocapacitors (combined) if we add another identical capacitor connected in series with the first one and keep the external voltage unchanged?

U2/U1 = ?

(b) What would be the energy U2 stored in two capacitors (combined) if we add another identical capacitor connected in parallel with the first one and keep the external voltage unchanged?

U2/U1 = ?

Students run their experiment by charging a capacitor. The voltage across the capacitor was increasing with time. In data analysis, they used computer and found a good fit for V(t) with the theoretical function for charging a capacitor: V(t) = A(1 - e-Ct) + B The result of the computer fit gave them the following numbers: A = 4.4; B = 0.0038; and C = 0.056 What is the value of the time constant tau? A capacitor is charged and the potential difference between its electrodes is equal to V0. The initial energy stored in this capacitor is U0. Next, the capacitor was partially discharged and the potential difference between the electrodes V was reduced to one half of the initial value V0. What was the change in electrical energy stored in the capacitor? U/U0 = ? A capacitor with capacitance C is completely charged using an external voltage V. The energy stored in this capacitor is equal to U1 = CV2/2. What would be the energy U2 stored in twocapacitors (combined) if we add another identical capacitor connected in series with the first one and keep the external voltage unchanged? U2/U1 = ? What would be the energy U2 stored in two capacitors (combined) if we add another identical capacitor connected in parallel with the first one and keep the external voltage unchanged? U2/U1 = ?

Explanation / Answer

1) time constant = 1/C =17.9 s

2) change in electrical energy stored in the capacitor = Uo/4 - Uo = -(3/4)* Uo

U/Uo = 1/4

3) a) 1/2 (C2= C/2)

b) 2 (C2 = 2C)

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