Question

Regarding the units involved in the relationship τ=RC, verify that the units of resistance times capacitance are time, that is, Ω⋅F=s.

a) True
b) False

Answer 1

The units of resistance times capacitance in the equation T=RC are in fact time, as demonstrated by substituting the units into the equation and simplifying.

Step-by-step explanation:

The units involved in the relationship T=RC are resistance (R) in ohms (Ω) and capacitance (C) in farads (F). To verify that the units of resistance times capacitance are time, we can substitute the units into the equation:

T = R * C

Using the given values for resistance and capacitance, we have:

T = (1.00 × 10³ Ω) * (8.00 µF)

Since 1 F = 1 s/Ω, the units simplify to:

T = (1.00 × 10³ Ω) * (8.00 µF) = 8.00 ms

Therefore, the units of resistance times capacitance, when substituted into the equation, yield a time unit.