Answer :
The value of the third capacitance is determined as 8 μF.
How calculate the third capacitance?
The value of the third capacitance is calculated by applying the following formula as shown below.
The formula for energy stored in a capacitor;
E = ¹/₂ CV²
where;
- C is the equivalent capacitance of the four capacitors
- V is the voltage in the circuit
The equivalent capacitance of the four capacitors in parallel is calculated as;
CV² = 2E
C = 2E/V²
C = ( 2 x 2.7 x 10⁻³ ) / ( 15²)
C = 2.4 x 10⁻⁵ F
C = 24 x 10⁻⁶ F
C = 24 μF
The value of the third capacitance is calculated as;
C3 = C - (C1 + C2 + C4)
C3 = 24 μF - (4μF + 4μF + 8μF)
C3 = 8 μF
The complete question is below:
Four capacitors are in parallel, C1, C2, C3, and C4. If C1=C2=4.00μF and C4=8.00μF, what should the capacitance C3 be for the network to store 2.70×10⁻³J of electrical energy at a 15 Volts?
