   Chapter 18, Problem 32P

Chapter
Section
Textbook Problem

Show that τ = RC has units of time.

To determine
whether the time constant τ has unit of time.

Explanation

Given Info:

Explanation:

Formula to calculate the time constant τ

τ=RC (I)

• τ is the time constant,
• R is the resistance,
• C is the capacitance,

Consider unit for R isohm, unit forVisvolt, unit for I isampere, and unit for Q is coulomb.

The formula for resistance R is,

R=VI

Substitute the ohmfor R and, volt for V, to find R

R=voltampere (II)

The formula for capacitance C is,

C=QV

Substitute, voltforV, and Coulomb for Q, to find C

C=Coulombvolt (III)

The formula for current I is,

I=dQdt

Substitute, ampere for I , Coulomb for dQ, andsecond for dt to find ampere

ampere=</

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