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Capacitance (C) is measured in farads, where 1 farad is equivalent to 1 coulomb per volt. Resistance (R) is measured in ohms, and 1 ohm is equal to 1 volt per ampère. The coulomb is defined as the amount of charge passing when a current of 1 ampère flows for 1 second. What is the unit of RC expressed in its simplest form?

Sagot :

secydemon
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MrRoyal

When fundamental units are combined, they result in derived units. RC (which means Resistance Capacitance) is a derived unit and its unit in the simplest form is Coulomb per Ampere (C/A)

Given that:

Capacitance (C) [tex]\to[/tex] Farads (f)

and

[tex]1f = 1\frac CV[/tex] ----- 1 farad = 1 capacitance per volt

Resistance (R) [tex]\to[/tex] Ohms [tex]\Omega[/tex]

[tex]1 \Omega = 1\frac{V}{A}[/tex]

The unit of RC is the product of the unit of R by the unit of C.

i.e.

[tex]RC = 1f \times 1\Omega[/tex]

Substitute [tex]1f = 1\frac CV[/tex]

[tex]RC = 1\frac CV \times 1\Omega[/tex]

Substitute [tex]1 \Omega = 1\frac{V}{A}[/tex]

[tex]RC = 1\frac CV \times 1\frac VA[/tex]

Cancel out volts (V)

[tex]RC = 1\frac CA[/tex]

[tex]\frac CA[/tex] means Coulomb per Ampere

Hence, the unit of RC is Coulomb per Ampere.

Read more about units at:

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