The capacitor of a capacitance 20microfarad and30microfarad are connected in parallel and the parallel pair that is formed is connected in series with a 5.0micro farad capacitor @: represent in a diagram b: prove that the potential difference across each capacitor is 5v c: determine the charge stored in each capacitor
a) Representation in a diagram: To represent the given circuit in a diagram, use the following notation:
- For the 20μF capacitor: C1
- For the 30μF capacitor: C2
- For the 5.0μF capacitor: C3
The circuit can be represented as:
--------C1----------
|
---C2---C3---
Here, C1 and C2 are connected in parallel, and the parallel combination is connected in series with C3.
b) To prove that the potential difference across each capacitor is 5V, we need to apply the principles of parallel and series connections in capacitors.
In a parallel connection, the potential difference across each component is equal. Therefore, the potential difference across C1 and C2 will be the same. Let's call this potential difference Vp.
In a series connection, the total potential difference is the sum of the potential differences across each component. Therefore, the potential difference across C3 will be the sum of Vp and the potential difference across C1 and C2. Let's call this potential difference Vs.
Given that C1 and C2 are connected in parallel, the total capacitance Cp of the parallel combination is:
Cp = C1 + C2
= 20μF + 30μF
= 50μF
Now, using the formula for the capacitance of series-connected capacitors, we can find Vs:
1/Cs = 1/Cp + 1/C3
Given: Cp = 50μF and C3 = 5.0μF
Substituting the values:
1/Cs = 1/50μF + 1/5.0μF
1/Cs = (1 + 10)/50μF
1/Cs = 11/50μF
Cs = 50μF/11
Let's assume Cs ≈ 4.545μF
Now, we can find Vs using the formula for the potential difference across series-connected capacitors:
Vs = (C3 / Cs) * Vp
Substituting the values:
Vs = (5.0μF / 4.545μF) * Vp
Vs = 1.1 * Vp
From this equation, it is clear that the potential difference across C1 and C2 is equal to Vp, and the potential difference across C3 is 1.1 times Vp.
c) To determine the charge stored in each capacitor, we need to use the formula for the charge stored in a capacitor:
Q = C * V
For C1 and C2: Since the potential difference across each capacitor is 5V (Vp), the charge stored in each capacitor can be calculated as:
Q1 = C1 * Vp
= 20μF * 5V
= 100μC
Q2 = C2 * Vp
= 30μF * 5V
= 150μC
For C3: Since the potential difference across C3 is 1.1 times Vp, the charge stored in C3 can be calculated as:
Q3 = C3 * Vs
= 5.0μF * 1.1 * Vp
= 5.5μF * Vp
= 5.5μF * 5V
= 27.5μC
Therefore, the charge stored in each capacitor is as follows:
- Q1 = 100μC (for C1)
- Q2 = 150μC (for C2)
- Q3 = 27.5μC (for C3)