What is the reactance of a capacitor of .005 farads at a frequency of 1000 Hz?

What is the reactance of a capacitor of .005 farads at a frequency of 1000 Hz?

• A. 1.59 K ohms
• B. 2.62 K ohms
• C. 3.18 K ohms
• D. 4.75 K ohms

Answer: (C)

To calculate the reactance of a capacitor, you can use the formula: \[ X_C = \frac{1}{2 \pi f C} \] where: - \(X_C\) is the capacitive reactance, - \(f\) is the frequency in hertz (Hz), - \(C\) is the capacitance in farads (F). In this case, the capacitor has a capacitance of 0.005 farads and we are working with a frequency of 1000 Hz. Plugging these values into the formula: 1. Calculate \(2 \pi f\): \[ 2 \pi (1000) \approx 6283.19 \] 2. Now substitute this into the formula to find \(X_C\): \[ X_C = \frac{1}{6283.19 \cdot 0.005} \] 3. Performing the calculation: \[ X_C = \frac{1}{31.41595} \approx 0.03183 \] 4. Convert this into ohms (keeping in mind it is expressed in kilohms): \[ X_C \approx 31.83 \, \text{ohms

To calculate the reactance of a capacitor, you can use the formula:

[

X_C = \frac{1}{2 \pi f C}

]

where:

• (X_C) is the capacitive reactance,

• (f) is the frequency in hertz (Hz),

• (C) is the capacitance in farads (F).

In this case, the capacitor has a capacitance of 0.005 farads and we are working with a frequency of 1000 Hz. Plugging these values into the formula:

1. Calculate (2 \pi f):

[

2 \pi (1000) \approx 6283.19

]

2. Now substitute this into the formula to find (X_C):

[

X_C = \frac{1}{6283.19 \cdot 0.005}

]

3. Performing the calculation:

[

X_C = \frac{1}{31.41595} \approx 0.03183

]

4. Convert this into ohms (keeping in mind it is expressed in kilohms):

[

X_C \approx 31.83 , \text{ohms