Question

4.2.2 What is an RC Circuit?

Recall that the capacitance is defined as the proportionality constant between the total charge accumulated by a capacitor and the voltage difference across the circuit

Q = C△V (4.2)

In this equation, the charge Q is expressed in Coulomb (C), the voltage △V, in volts (V) and the capacitance C in farads (F).

In this lab you will study both the charging and discharging process of an RC circuit. During the charging process, an electrical EMF source accumulates charges on each side of the parallel plate capacitor. During the discharging process, the capacitor releases all its charges into the circuit (which now does not contain the battery). Capacitors charge and discharge exponentially in time. During the discharge of a capacitor, the instantaneous voltage △Vc between the ends of the capacitor also drops and is given by △Vс = △Vmax*e^(-t/τ) (4.3) where △Vmax is the maximum voltage across the capacitor, i.e. the voltage to which thecapacitor was initially charged, t is the time and τ is the time constant given by τ= Req*Ceq (4.4) where Req and Ceq are, respectively, the equivalent resistance and capacitance to which we can reduce the circuit. Although the theoretical discharge time is in nite, in practice we consider that the discharge is over when the voltage at the bounds of the capacitor is at 1% of its maximal value.

Answer the following questions in the Results section: Assuming the voltage, when completely charged, is set to V₀ = 1 and by considering the variables τ for time constant and t for time, what are the equations for of charging and discharging? Support your answer by physical arguments

Answer 1

(4.2.2) What is an RC Circuit?

A resistor-capacitor circuit or RC network, is an electric circuit composed of resistors and capacitors which driven by a voltage or current source.

Mathematically, we have

= R C

We know tha, the capacitance is defined as "the proportionality constant between the total charge accumulated by a capacitor and the voltage difference across a circuit".

Mathematically, we have

Q = C V

where, Q = charge expressed in Coulomb (C),

V = voltage difference expressed in Volts (V)

C = capacitance expressed in Farads (F)

Answer the following questions in a Results section :

The equations for charging which will be given as -

V_C = V₀ (1 - e^-/t)

where, V₀ = maximum voltage across the capacitor = 1

= time constant = R C

t = elapsed time

then, we get

V_C = (1 V) (1 - e^-/t)

The equations for discharging which will be given as -

V_C = V₀ . e^-/t

where, V₀ = maximum voltage across the capacitor = 1

= time constant = R C

t = elapsed time

then, we get

V_C = (1 V) . e^-/t