Two capacitors of capacitance C_5 = 6.00 \rm \mu F and C_6 = 3.00 \rm \mu F are added to the network, as shown in the diagram. (Part B figure) Find the equivalent capacitance C_B of the new network of capacitors.
I don't see your diagram and I don't know what your \rm symbol is supposed to mean.
This is preswumably an exercise in computing the equivalent capacitance of a pair of capacitors in series or in parallel.
In parallel, the capacitances add.
In series, the reciprocal capacitances add.
To find the equivalent capacitance C_B of the new network of capacitors, we can use the following formula:
1/C_B = 1/C_5 + 1/C_6
First, let's substitute the values of C_5 and C_6 into the equation:
1/C_B = 1/6.00 μF + 1/3.00 μF
To add these fractions together, we need a common denominator. In this case, we can use 6.00 μF as the common denominator:
1/C_B = (1/6.00 μF) + (2/6.00 μF)
Now, let's combine the fractions:
1/C_B = (3/6.00 μF)
To simplify the equation further, we can invert both sides:
C_B = (6.00 μF) / (3/6.00 μF)
Dividing by a fraction is the same as multiplying by its reciprocal:
C_B = (6.00 μF) * (6.00 μF/3)
Multiplying the numerators and the denominators:
C_B = (6.00 μF * 6.00 μF) / 3
= 36.00 μF^2 / 3
Finally, let's simplify the expression:
C_B = 12.00 μF
Therefore, the equivalent capacitance C_B of the new network of capacitors is 12.00 μF.