Question

If c1=c2=4. 00μf and c4=8. 00μf, what must the capacitance c3 be if the network is to store 2. 70×10−3 j of electrical energy?

Answer 1

To find the capacitance c3 that the network should have in order to store 2.70 x 10^-3 J of electrical energy, we can use the formula for electrical energy stored in a capacitor, U = (1/2) * C * V^2. Using the given values of c1, c2, and c4, we can calculate the equivalent capacitance c_eq of the network and then solve for c3.

Step-by-step explanation:

To find the capacitance c3 that the network should have in order to store 2.70 x 10^-3 J of electrical energy, we can use the formula for electrical energy stored in a capacitor, U = (1/2) * C * V^2, where U is the energy, C is the capacitance, and V is the voltage. In this case, since c1 = c2 = 4.00μF and c4 = 8.00μF, we can calculate the equivalent capacitance c_eq of the network by using the formula for capacitors in series, 1/c_eq = 1/c1 + 1/c2 + 1/c3 + 1/c4. Once we have c_eq, we can solve for c3.

Let's first calculate c_eq.

1/c_eq = 1/c1 + 1/c2 + 1/c3 + 1/c4

1/c_eq = 1/4.00μF + 1/4.00μF + 1/c3 + 1/8.00μF

1/c_eq = 0.25μF + 0.25μF + 1/c3 + 0.125μF

1/c_eq = 0.625μF + 1/c3

1/c_eq - 0.625μF = 1/c3

Now we can substitute c_eq and solve for c3.

1/c3 = 1/c_eq - 0.625μF

1/c3 = 0.625μF

c3 = 1 / (0.625μF)

c3 = 1.60μF