Time Dependent Circuits: RC in Series

Laboratory report №8
Title: Time Dependent Circuits: RC in Series
Section №10
Date: 11.04.2022
Aruzhan Gabit
Aruzhan Oralkhanova
Adelina Zeinolla

Objectives:
● To examine and to practice using RC circuits;
● To find and compare the time constant of RC circuit using two methods: from resistance
and capacitance values and from exponential charging and discharging curves;
● To evaluate two methods of finding time constant of the RC circuits.

I. Experimental description




Figure 1. RC circuit setup for the experiment.

II. Experimental data
Table 1. Values of the resistance and capacitance measured using multimeter.
Capacitance C, μF Resistance R, kΩ Initial voltage Vo , V

998±0.5 14.93±0.005 5.00

, III. Data analysis
Formula derivations
Theoretical time constant τ can be expressed as a product of the RC circuit resistance and
capacitance values:
τ=𝑅 ×𝐶 (1)
where,
τ - time constant, s
𝑅 - resistance, Ω
𝐶 - capacitance, C

During the charging process, the voltage across the capacitor increases, while voltage across the
resistor increases. This relationship can be expressed as
𝑡
−τ
𝑉𝐶(𝑡) = 𝑉0(1 − 𝑒 ) (2)
𝑡
−τ
𝑉𝑅(𝑡) = 𝑉0𝑒 (3)
where,
𝑉𝐶 - voltage across the capacitor, V
𝑉𝑅 - voltage across the resistor, V
𝑉0 - initial voltage, V
t - time, s

During the discharging process, since supply voltage is reduced, the capacitor begins to
discharge in the opposite direction. Therefore, voltages across the capacitor and resistor can be
expressed as
𝑡
−τ
𝑉𝐶(𝑡) = 𝑉0𝑒 (4)
𝑡
−τ
𝑉𝑅(𝑡) = − 𝑉0𝑒 (5)
By adjusting equations (2) and (4) for the charging and discharging graphs, it is evident that the
slope of both is equal to the reciprocal of time constant. Therefore, time constant can be found by
taking the reciprocal of the slope. That is,
1
τ= (6)
𝑠𝑙𝑜𝑝𝑒
Error propagation
Error in theoretical time constant:
2 2
∆τ = ( ∂τ
∂𝐶
∆𝐶 ) +( ∂τ
∂𝑅
∆𝑅) =
2
(𝐶∆𝑅) + (𝑅∆𝐶)
2
(7)
Error in experimental time constant:
2
∆τ = ( ∂τ
∂𝑠𝑙𝑜𝑝𝑒
∆𝑠𝑙𝑜𝑝𝑒 ) (8)