Calculate the equivalent capacitance between points a and b for each of the two networks shown in the figure below. Each capacitor has a capacitance of 9.52 µF. (Give your answers to at least two decimal places.)
www.webassign.net/katzpse1/27-p-021.png
To calculate the equivalent capacitance between points a and b for each network, we can use the concept of series and parallel combinations of capacitors.
For the first network:
Since the two capacitors (each with a capacitance of 9.52 µF) are in parallel, their equivalent capacitance can be calculated using the formula:
1/Ceq = 1/C1 + 1/C2
Substituting the values:
1/Ceq = 1/9.52 µF + 1/9.52 µF
Now, we can calculate the equivalent capacitance (Ceq) by taking the reciprocal of the sum of the reciprocals:
1/Ceq = 1/9.52 µF + 1/9.52 µF
1/Ceq = 2/9.52 µF
To find the value of Ceq, we take the reciprocal of both sides:
Ceq = 9.52 µF/2
Calculating this expression, we get:
Ceq = 4.76 µF
Therefore, the equivalent capacitance between points a and b in the first network is 4.76 µF.
For the second network:
In this network, the two capacitors are in series. To find the equivalent capacitance, we use the formula:
Ceq = C1 + C2
Substituting the values:
Ceq = 9.52 µF + 9.52 µF
Ceq = 19.04 µF
Therefore, the equivalent capacitance between points a and b in the second network is 19.04 µF.
To calculate the equivalent capacitance between points a and b for each network, we can use the formula for capacitors in series and parallel.
For the network on the left:
We see that the two capacitors are in parallel, so their equivalent capacitance can be found by summing their individual capacitances.
C_eq1 = C1 + C2 = 9.52 µF + 9.52 µF = 19.04 µF
For the network on the right:
We can see that the two capacitors are in series, so their equivalent capacitance can be found using the formula:
1/C_eq2 = 1/C1 + 1/C2
1/C_eq2 = 1/9.52 µF + 1/9.52 µF
1/C_eq2 = 2/9.52 µF
C_eq2 = 9.52 µF/2 = 4.76 µF
Therefore, the equivalent capacitance between points a and b for the network on the left is 19.04 µF, and for the network on the right, it is 4.76 µF.