We are given the following circuit with capacitors , , and with a total applied voltage .
Step 1: Simplifying the circuit
- First, we need to combine the capacitors in series and parallel. - The first two capacitors and are in series, so their equivalent capacitance is given by the formula for capacitors in series: Substituting the values of and : So, .
Step 2: Combine the equivalent capacitor with
- Now, is in parallel with , so the total equivalent capacitance of the entire system is:
Step 3: Calculate the total charge stored
- The total charge stored in the system is given by the formula: Substituting the values and :
Step 4: Calculate the individual charges
- The charge stored in the capacitors depends on the voltage across them. - The voltage across and is the same since they are in series. - The voltage across the parallel combination is the same, so: Thus, the charges are 24 C, 48 C, and 216 C respectively.