How to Solve Capacitor Circuits

Step-by-Step Guide

1. 1

   Step 1: Identify the circuit.

   A series circuit has only one loop with no branching paths.
   
   Capacitors in the circuit are arranged in order within the same loop. , Given the voltage and capacitor values for each, find the total capacitance.
   
   To calculate the total capacitance in a series circuit, use the formula 1CT=1C1+1C2+1C3{\displaystyle {\frac {1}{C_{T}}}={\frac {1}{C_{1}}}+{\frac {1}{C_{2}}}+{\frac {1}{C_{3}}}}.
   
   For example:
   A series circuit has three different capacitors of value C1 = 2F, C2 = 3F, C3 = 6F.
   
   Plug in to the formula 1CT=12+13+16{\displaystyle {\frac {1}{C_{T}}}={\frac {1}{2}}+{\frac {1}{3}}+{\frac {1}{6}}} and solve for CT.
   
   Adding the fraction and taking the inverse, CT = 1F. , The total charge in a circuit depends on the total voltage and the total capacitance in a circuit.
   
   This relationship is given by the equation Q=CV{\displaystyle Q=CV}.
   
   For example:
   The circuit has a total capacitance of 1 F and total voltage of 10 V.
   
   Plug in the given to the equation and solve for Q:
   Q=1∗10=10C{\displaystyle Q=1*10=10C} , For a series circuit, charge across each capacitor is the same and equal to the total charge in the circuit.
   
   For example:
   The total charge in the circuit is 10 C.
   
   Then the charge in C1 is 10 C, C2 is 10 C and C1 is 10C. , Rearranging the equation Q=CV{\displaystyle Q=CV} to V=Q/C{\displaystyle V=Q/C}, the voltage across each capacitor can be calculated.
   
   For Example:
   The charge is 10 C for all capacitors and capacitance values are 2 F, 3 F and 6 F respectively.
   
   Voltage across first capacitor is V1 = Q1/C1 = 10/2 = 5V Voltage across second capacitor is V2 = Q2/C2 = 10/3 =
   3.3V Voltage across third capacitor is V3 = Q3/C3 = 10/6 =
   1.7 V Note that the sum of individual voltage equals the total voltage in the series circuit. , Once the voltage and charge in each capacitor is calculated, the circuit is solved.
   
   Label these information in the circuit drawing to keep everything organized. .
2. 2

   Step 2: Calculate the total capacitance.

3. 3

   Step 3: Calculate the total charge.

4. 4

   Step 4: Find the charge in each capacitor.

5. 5

   Step 5: Calculate the voltage across each capacitor.

6. 6

   Step 6: Draw and label each capacitor with its charge and voltage.

Detailed Guide

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