Reactance of a capacitor of capacitance C μ F for A C frequency (400/π) Hz is 25 Ω, the value of C is:

Question

Reactance of a capacitor of capacitance C μ F for A C frequency (400/π) Hz is 25 Ω, the value of C is: (A)  75 μ F  (B)  100 μ F  (C)  25 μ F  (D)  50 μ F

Tardigrade Admin · Accepted Answer

Capacitive reactance XC is given by XC=(1/ω C)=(1/2 π f C) where, ω=2 π f Given, XC=25 Ω, f=(400/π) H z Hence, 25=(1/2 π × (400)π × C) ⇒ C=(1/25 × 800)=50 μ F

Q. Reactance of a capacitor of capacitance $C μ F$ for $A C$ frequency $\frac{400}{π} Hz$ is $25 Ω$ , the value of $C$ is:

$75 μ F$

$100 μ F$

$25 μ F$

$50 μ F$

Capacitive reactance $X_{C}$ is given by
$X_{C} = \frac{1}{ω C} = \frac{1}{2 π f C}$
where, $ω = 2 π f$
Given, $X_{C} = 25 Ω, f = \frac{400}{π} Hz$
Hence, $25 = \frac{1}{2 π \times \frac{400}{π} \times C}$
$\Rightarrow C = \frac{1}{25 \times 800} = 50 μ F$

Q. Reactance of a capacitor of capacitance CμF for AC frequency π400​Hz is 25Ω, the value of C is:

75μF

100μF

25μF

50μF