Two parallel plate capacitors are identical, except that one of them is empty and the other contains a material with a dielectric constant of 4.2 in the space between the plates. The empty capacitor is connected between the terminals of an ac generator that has a fixed frequency and rms voltage. The generator delivers a current of 0.24 A. What current does the generator deliver after the other capacitor is connected in parallel with the first one?
Xc = 1/(2pi*F*C).
When an identical capacitor is placed in
parallel, the capacitance doubles and the reactance(Xc) is 1/2. Therefore, the current is doubled:
I = 2 * 0.24 = 0.48A.
To determine the current delivered by the generator after the other capacitor is connected in parallel, we need to analyze the effect of the dielectric material on the capacitance and subsequently on the current.
1. Start by considering the empty capacitor connected to the AC generator.
- Let's assume the empty capacitor has a capacitance of C (in Farads).
- The AC generator produces an RMS voltage, denoted as V (in Volts).
- The generator delivers a current of I1 (in Amperes) when only the empty capacitor is connected.
2. Now, introduce the second capacitor with the dielectric material.
- The dielectric material has a dielectric constant, denoted as κ (in this case, κ = 4.2).
- Since the capacitors are identical, the second capacitor also has a capacitance of C.
3. Connecting the capacitors in parallel results in an effective capacitance.
- When capacitors are connected in parallel, the total capacitance is the sum of the individual capacitances.
- Therefore, the effective capacitance when both capacitors are connected in parallel is 2C.
4. Analyzing the effect of capacitance on current.
- The current delivered by the AC generator is given by the formula: I = V / Xc, where Xc is the capacitive reactance.
- The capacitive reactance is inversely proportional to the capacitance: Xc = 1 / (2πfC), where f is the frequency of the AC generator.
5. Comparing the current before and after connecting the capacitors.
- Before connecting the two capacitors, the current delivered by the AC generator is I1.
- After connecting the capacitors in parallel, the effective capacitance becomes 2C, which affects the capacitive reactance, Xc, and subsequently, the current delivered by the AC generator.
To find the current delivered by the generator after the other capacitor is connected, we need information about the frequency of the AC generator and the value of one of the variables (either capacitance, voltage, or current).