need help on physics problem?

Question

(1) dQ/dt = -Q/RC
(2)Q=Qoe^-t/RC note:Qo is the initial charge.

For equation 2 is called the solution, because when Q(t) is plug into equation 1, the left side will equal to the right side.

How do i demonstrate that RC has the dimensions of time?

Answer 1

Good old unit conversion

1 ohm=V/I where I is in units of amp (A)
so ohm has units of V/A
1 Joule is the work required to carry 1 coulomb through 1 volt

so a volt has units of J/q where q is coulombs
therefore R has units of
J/(q*A)
a joule also has units of kg*m^2/s^2
since work = force times distance (m) and force equals mass (kg) times acceleration (m/s^2)

so rewrite R as
kg*m^2/(s^2*q*A)

a farad (C) has units of s^4*A^2/(kg*m^2)
multiply R*C

(kg*m^2/(s^2*q*A))*(s^4*A^2/(kg*m^2))
simplify
s^2*A/q
(s^2/q)*(q/s)
an AMP has units of q/s

so RC has units of seconds

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