Math Problem Statement

205.4 µF and 8 µF capacitors are connected with a 100V battery in parallel. What is the total charge stored by the capacitors?

Solution

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Problem 205: Two capacitors with capacitances of 4.4 µF and 8 µF are connected in parallel with a 100V battery. What is the total charge stored by the capacitors?

Solution: In a parallel combination, the total charge QtotalQ_{\text{total}} is given by: Qtotal=Ctotal×VQ_{\text{total}} = C_{\text{total}} \times V Where Ctotal=C1+C2C_{\text{total}} = C_1 + C_2 (since it's a parallel circuit).

  1. C1=4.4μF=4.4×106FC_1 = 4.4 \, \mu F = 4.4 \times 10^{-6} \, F
  2. C2=8μF=8×106FC_2 = 8 \, \mu F = 8 \times 10^{-6} \, F
  3. V=100VV = 100 \, V

Now, Ctotal=4.4×106+8×106=12.4×106FC_{\text{total}} = 4.4 \times 10^{-6} + 8 \times 10^{-6} = 12.4 \times 10^{-6} \, F Then, the total charge QtotalQ_{\text{total}}: Qtotal=12.4×106×100=12.4×104C=1.24×103C=12.4mCQ_{\text{total}} = 12.4 \times 10^{-6} \times 100 = 12.4 \times 10^{-4} \, C = 1.24 \times 10^{-3} \, C = 12.4 \, mC

So, the closest answer seems to match option (3).


Would you like to proceed with more problems or need further explanation?

Here are five related questions for further exploration:

  1. How do capacitors behave differently when arranged in series versus parallel?
  2. What is the formula for calculating the equivalent capacitance in series?
  3. How does the stored energy in a capacitor change with voltage?
  4. Why is the total charge different in series versus parallel connections?
  5. What is the physical meaning of capacitance?

Tip: Remember that the capacitance in parallel adds up, whereas in series, the reciprocal sum determines the total capacitance.

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Math Problem Analysis

Mathematical Concepts

Capacitance
Parallel Circuits
Charge Calculation

Formulas

Q = C_total × V
C_total = C1 + C2 (for parallel circuits)

Theorems

Capacitance in Parallel Circuits

Suitable Grade Level

Grades 10-12