Part C – RC Circuits in AC Mode 1. Derive Equation 5-6 from Equation 5-5. 2. Using the τ’s you calculated and your measured resistance: a. Calculate the capacitances of the capacitors. b. Compare your calculated and measured values via percent error.

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1) attached below

2) a)  31 Ω,   302.9 Ω

   b)  17.3 Ω ,  26.4 Ω

Explanation:

1) Deriving Eqn 5-6 from Eqn 5-5

attached below

2) using τ’s calculated and measured resistance

use given data

Tm1 = Rm1 * Cm1

       = 329.3 * 333 * 10^-9 = 109.65 μs

Tm2 = Rm2 * Cm2

       = 329.3 * 200 * 10^-9 = 658.6 μs

a) Capacitance of capacitors

For Cm1

   t₁₂ = 72 μs = R₁' Cm1 log²

 ∴ R₁' = ( 72 * 10^-6 ) / ( 333 * 10^-9 log² )

         = 31 Ω

For Cm2

 t₁₂ = 40 μs  , ∴  R₂' = 302.9 Ω

b) comparing calculated and measured values via percent error

errors

Rm1 - R₁' = 17.3 Ω

Rm2 - R₂' = 26.4 Ω

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explanation:

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c) up

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