An isolated capacitor of unknown capacitance has been charged to a potential difference of 100 V. When the charged capacitor is then connected in parallel to an un-
charged 10.0 μF capacitor, the potential difference across the combination is 30.0 V.
Calculate the unknown capacitance.
10.0µF=10*10^-6F. C=Q/V => c=(10*10^-6)/70= unknown capactitance?
Im guessing this is it?
C = Q / 100...100 C = Q
capacitors add in parallel
the charge is the same (redistributed)
C + 10 = 100 C / 30
solve for C
Well, I must say, dealing with unknowns can be quite shocking! But fear not, I'm here to clown around and help you out.
To calculate the unknown capacitance, we need to use the formula for capacitors in parallel. Since the potential difference across the combination is 30.0 V, the total charge remains the same when capacitors are connected in parallel.
So, using the formula C = Q/V, where Q is the charge and V is the potential difference, we have:
10.0 μF * (100 V) = C * (30.0 V)
Simplifying the equation, we find:
10.0 μC = 3C
Now, let's solve for C:
C = 10.0 μC / 3
C = 3.33... μF
So, the unknown capacitance is approximately 3.33 microfarads. Watch out for those sneaky unknowns, they can really spark curiosity!
Not quite. Let's go through the calculation step-by-step to find the unknown capacitance.
1. The equation for the equivalent capacitance of capacitors in parallel is given by:
C_eq = C_1 + C_2
where C_eq is the equivalent capacitance and C_1 and C_2 are the individual capacitances.
2. In this case, we have an uncharged capacitor of 10.0 μF (or 10 * 10^-6 F) connected in parallel to the isolated capacitor of unknown capacitance.
Therefore, the equivalent capacitance is:
C_eq = C_unknown + 10.0 μF
3. We are given that when the charged capacitor is connected in parallel to the uncharged capacitor, the potential difference across the combination is 30.0 V.
The total charge is conserved in a parallel circuit, so we can use the formula:
Q = C_eq * V
where Q is the charge, V is the potential difference, and C_eq is the total capacitance.
4. Substituting the given values:
Q = (C_unknown + 10.0 μF) * 30.0 V
5. Since the charged capacitor has been connected to the uncharged capacitor, the total charge Q is the same for both capacitors.
The charge on the capacitor that was initially charged to 100 V is given by:
Q = C_initial * V_initial
where C_initial is the initial capacitance and V_initial is the initial potential difference.
Substituting the given values:
Q = C_unknown * 100 V
6. Equating the two expressions for charge:
C_unknown * 100 V = (C_unknown + 10.0 μF) * 30.0 V
7. Solving this equation for C_unknown:
100 V * C_unknown = 30.0 V * C_unknown + 300.0 μC
70.0 V * C_unknown = 300.0 μC
C_unknown = 300.0 μC / 70.0 V
C_unknown ≈ 4.29 μF
So, the unknown capacitance is approximately 4.29 μF.
To calculate the unknown capacitance, we will use the principle of conservation of charge.
1. Start by calculating the charge on the known capacitor, which is connected in parallel to the unknown capacitor. We know that the potential difference across the combination of capacitors is 30.0 V. Therefore, the charge on the known capacitor can be calculated using the formula Q = C * V, where Q is the charge, C is the capacitance, and V is the potential difference.
Given: Capacitance (C1) = 10.0 μF = 10 * 10^-6 F, Potential difference (V) = 30.0 V.
Q1 = (10 * 10^-6 F) * (30.0 V) = 3.0 * 10^-4 C
2. According to the principle of conservation of charge, the charge on the known capacitor will be equal to the sum of the charges on both capacitors when they are connected in parallel. Therefore, the charge on the unknown capacitor (Q2) can be calculated as:
Q2 = Q1
Q2 = 3.0 * 10^-4 C
3. Now, we can calculate the capacitance of the unknown capacitor (C2) using the formula C = Q / V:
C2 = Q2 / V
C2 = (3.0 * 10^-4 C) / (100 V) = 3.0 * 10^-6 F
Therefore, the unknown capacitance is approximately 3.0 μF.