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Chapter 4: Q19DQ (page 873)

Verify that the time constant RC has units of time.

Short Answer

Expert verified

The time constant RC has units of time.

Step by step solution

01

Time constant

The time constant for a capacitor is the time required by the capacitor to charge to 63.2 % of the applied voltage in the given circuit. it has the unit of time (s).

02

Step 2:Calculation of the unit of time constant

The self-capacitance of a conductor is;

C=qε

Here

  • The charge has a unit of coulomb (C)
  • Potential has a unit of a volt (V)
  • Capacitance has a unit of Farad (F);

The above expression can be written as:

Cunit=CV

Resistance of a conductor is:

R=εl

Here,

  • The resistance unit is ohm’s Ωand
  • the current unit is Coulomb (C) per second.

The above expression can be written as:

Runit=VC/s

From the above two equations, we can calculate the unit of time constant as:

RCunit=Runit×Cunit=VC/s×CV=s

Hence, the time constant RC has units of time (s).

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