# RC circuit and kirchoff's loop rule

• okgo
In summary, the conversation discusses the solution to Question 27, where the correct answer is A. However, the person is confused because they thought it would be B according to Korkoff's Loop rule. The conversation then goes on to explain the reasoning behind A being the correct answer, using equations and modeling a capacitor as an open circuit after an infinite amount of time. The final conclusion is that Vc equals half of Vb and is equal to Q/C.
okgo
http://www.screencast.com/users/trinhn812/folders/Jing/media/de5edaba-e848-47f5-82b9-bd770b216e95

I need help with Question 27 specifically. The correct answer is A, but I don't understand why.

I thought it would be B according to Korkoff's Loop rule of the inner left loop, where current of inner left loop is 0 after switch is closed after a long time. So V(battery) - Q/C = 0 so V(battery) =Q/C

Let's see here, it can't be a because the cap isn't in parallel with the battery. A capacitor has infinite impedance at DC, so after an infinite time it can be modeled as an open circuit.

So loop 1)
Vb-Vc-IR=0
Loop 2)
Vb-2IR=0

combine to get
Vb-Vc-Vb/2=0

so
Vc=Vb/2

Vc=Q/C

so Vb/2=Q/C

Q=C*Vb/2

Voila.

## 1. What is an RC circuit?

An RC circuit is a type of electrical circuit that contains a resistor and a capacitor. It is often used in electronic devices to control the flow of current and voltage.

## 2. How does an RC circuit work?

An RC circuit works by using the resistor to limit the flow of current and the capacitor to store and release electrical energy. The capacitor charges up when the circuit is turned on and discharges when the circuit is turned off, creating a time delay in the flow of current.

## 3. What is Kirchoff's loop rule?

Kirchoff's loop rule, also known as Kirchoff's voltage law, states that the sum of the voltage drops in a closed loop in a circuit must be equal to the sum of the voltage sources in that same loop.

## 4. How is Kirchoff's loop rule applied in RC circuits?

In an RC circuit, Kirchoff's loop rule is used to calculate the voltage drop across the resistor and capacitor. This helps in determining the time constant of the circuit and the behavior of the capacitor as it charges and discharges.

## 5. What is the significance of RC time constant in RC circuits?

The RC time constant, denoted by the symbol τ (tau), is a measure of how quickly a capacitor charges or discharges in an RC circuit. It is calculated by multiplying the resistance and capacitance values and represents the time it takes for the capacitor to charge up to 63.2% of its maximum charge or discharge to 36.8% of its initial charge.

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