If capacitors of 10 mfd, 5 mfd, and 5 mfd are wired in series, what is the total capacitance in mfd?

If capacitors of 10 mfd, 5 mfd, and 5 mfd are wired in series, what is the total capacitance in mfd?

• A. 20 mfd
• B. 2 mfd
• C. 10 mfd
• D. 5 mfd

Answer: (B)

When capacitors are wired in series, the total capacitance can be calculated using the formula for capacitors in series, which is: \[ \frac{1}{C_{\text{total}}} = \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3} \] In this case, you have three capacitors with values of 10 mfd, 5 mfd, and 5 mfd. Plugging these values into the series capacitance formula gives: \[ \frac{1}{C_{\text{total}}} = \frac{1}{10} + \frac{1}{5} + \frac{1}{5} \] To combine the fractions, you'll first convert them to a common denominator: \[ \frac{1}{10} + \frac{2}{10} + \frac{2}{10} = \frac{5}{10} = \frac{1}{2} \] Now, taking the reciprocal to find the total capacitance: \[ C_{\text{total}} = \frac{1}{\frac{1}{2}} = 2 \text{ m

When capacitors are wired in series, the total capacitance can be calculated using the formula for capacitors in series, which is:

[

\frac{1}{C_{\text{total}}} = \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3}

]

In this case, you have three capacitors with values of 10 mfd, 5 mfd, and 5 mfd. Plugging these values into the series capacitance formula gives:

[

\frac{1}{C_{\text{total}}} = \frac{1}{10} + \frac{1}{5} + \frac{1}{5}

]

To combine the fractions, you'll first convert them to a common denominator:

[

\frac{1}{10} + \frac{2}{10} + \frac{2}{10} = \frac{5}{10} = \frac{1}{2}

]

Now, taking the reciprocal to find the total capacitance:

[

C_{\text{total}} = \frac{1}{\frac{1}{2}} = 2 \text{ m