Two uncharged capacitor with C1 = 55 μF and C2 = 15 μF are connected in parallel to a battery with ε = 1.5 V. a)Calculate the numerical value of Q1 in μC. b) Calculate the numerical value of Q2 in μC. c) Express the total charge on the two capacitors in terms of C1, C2, and ε.
Two uncharged capacitor with C1 = 55 μF and C2 = 15 μF are connected in parallel to a battery with ε = 1.5 V. a)Calculate the numerical value of Q1 in μC. b) Calculate the numerical value of Q2 in μC. c) Express the total charge on the two capacitors in terms of C1, C2, and ε.
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Two uncharged capacitor with C1 = 55 μF and C2 = 15 μF are connected in parallel to a battery with ε = 1.5 V.
a)Calculate the numerical value of Q1 in μC.
b) Calculate the numerical value of Q2 in μC.
c) Express the total charge on the two capacitors in terms of C1, C2, and ε.
![The image depicts a simple electrical circuit diagram featuring capacitors in series with a voltage source.
- **C1 and C2**: These represent two capacitors connected in series within the circuit. Capacitors are components that store electrical energy in an electric field.
- **ε (Epsilon)**: This symbol represents a voltage source (battery) connected in series with the capacitors. The voltage source provides the electromotive force (EMF) that drives current through the circuit.
**Explanation**:
In this configuration, the total capacitance (C_total) of the series circuit is determined by the formula:
\[
\frac{1}{C_{\text{total}}} = \frac{1}{C_1} + \frac{1}{C_2}
\]
When capacitors are connected in series, the total capacitance is less than the smallest individual capacitor. This arrangement can be useful for specific applications where a specific capacitance or voltage rating is needed.
The voltage across each capacitor will add up to equal the total voltage supplied by the voltage source ε. The charge (Q) stored on each capacitor is the same, and it is determined by the formula:
\[
Q = C_{\text{total}} \times V
\]
where \( V \) is the total voltage of the source ε.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F279d9c1a-8686-4970-a64d-6e4fa13a7ad9%2Fbedfbe08-1389-4977-a91b-e11c727c13d8%2Fo8bbl8n_processed.png&w=3840&q=75)
Transcribed Image Text:The image depicts a simple electrical circuit diagram featuring capacitors in series with a voltage source.
- **C1 and C2**: These represent two capacitors connected in series within the circuit. Capacitors are components that store electrical energy in an electric field.
- **ε (Epsilon)**: This symbol represents a voltage source (battery) connected in series with the capacitors. The voltage source provides the electromotive force (EMF) that drives current through the circuit.
**Explanation**:
In this configuration, the total capacitance (C_total) of the series circuit is determined by the formula:
\[
\frac{1}{C_{\text{total}}} = \frac{1}{C_1} + \frac{1}{C_2}
\]
When capacitors are connected in series, the total capacitance is less than the smallest individual capacitor. This arrangement can be useful for specific applications where a specific capacitance or voltage rating is needed.
The voltage across each capacitor will add up to equal the total voltage supplied by the voltage source ε. The charge (Q) stored on each capacitor is the same, and it is determined by the formula:
\[
Q = C_{\text{total}} \times V
\]
where \( V \) is the total voltage of the source ε.
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