If a 1$\mu \mathrm { F }$, 2.2 $\mu F$ and 0.05 $\mu \mathrm { F }$ capacitor are connected in series, $\mathrm { C } _ { \mathrm { T } }$ is less than________
A) 0.001 $\mu \mathrm { F }$
B) 0.05$\mu \mathrm { F }$
C) 2.2 $\mu \mathrm { F }$
D) 1 $\mu \mathrm { F }$

Question

If a  1$\mu \mathrm { F }$, 2.2 $\mu F$ and  0.05 $\mu \mathrm { F }$ capacitor are connected in series, $\mathrm { C } _ { \mathrm { T } }$ is less than________
A)  0.001  $\mu \mathrm { F }$
B)  0.05$\mu \mathrm { F }$
C)  2.2  $\mu \mathrm { F }$
D)  1 $\mu \mathrm { F }$

Quizplus · Accepted Answer

When capacitors are connected in series, the total capacitance is less than any of the individual capacitances. The formula for calculating the total capacitance of capacitors connected in series is:
$$\frac{1}{C_T} = \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3} + \cdots$$
Plugging in the values given:
$$\frac{1}{C_T} = \frac{1}{1\mu F} + \frac{1}{2.2\mu F} + \frac{1}{0.05\mu F}$$
$$\frac{1}{C_T} = 0.4545 + 0.4545 + 20$$
$$\frac{1}{C_T} = 20.909$$
$$C_T = 0.0479\mu F < 0.05\mu F$$
Therefore, the answer is B.

If a 1 μF\mu \mathrm { F }μF , 22 μF\mu FμF

If a 1 $\mu \mathrm { F }$ , 22 $\mu F$