Question

What capacitance should be used to produce a\(2.00\,{\rm{M\Omega }}\)reactance at\(60.0\,{\rm{Hz}}\)?

Short answer

The capacitance used to produce a reactance is obtained as, \(1.33\,{\rm{nF}}\).

Step-by-step solution

Identification of the given data

The given data can be listed below as,

• The capacitance resistance is,\({X_C} = 2.00\,{\rm{M\Omega }}\).
• The frequency is, \(f = 60.0\,{\rm{Hz}}\).

Definition of capacitance

The capacity of a component or circuit to gather and hold energy in the form of an electrical charge is known as capacitance. Devices that store energy include capacitors, which come in a variety of sizes and forms.

Evaluating the inductive resistance

The inductive reactance is evaluated using the formula:

\({X_C} = \frac{1}{{2\pi fC}}\)

Solving for the capacity as:

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

Substitute all the value in the above equation.

\(\begin{aligned} L &= \frac{1}{{2\pi \times 60.0\,{\rm{Hz}} \times 2 \times {{10}^6}\,{\rm{\Omega }}}}\\ &= 1.33\,{\rm{nF}}\end{aligned}\)

Therefore, the capacitance used to produce a reactance is, \(1.33\,{\rm{nF}}\).