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### College Physics (Urone)

Book edition 1st Edition
Author(s) Paul Peter Urone
Pages 1272 pages
ISBN 9781938168000

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

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

See the step by step solution

## Step 1: 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, $$f = 60.0\,{\rm{Hz}}$$.

## Step 2: 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.

## Step 3: 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, $$1.33\,{\rm{nF}}$$.