Finding Voltage Across A Resistor in a 1st Order RC Circuit

In summary, a first order RC circuit is an electrical circuit consisting of a resistor and a capacitor connected in series. The voltage across the resistor can be calculated using Ohm's Law and is affected by the resistance, capacitance, and frequency of the circuit. The voltage across the resistor decays over time as the capacitor charges up, and it cannot be negative as it always follows the direction of current flow.
  • #1
Jon08CO
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Homework Statement



For the RC Circuit (R = 100 Ohm, C = 100 Micro Farads, and an open switch at t=0), we know that the capacitor is charged to a voltage of 10 V prior to T=0.

Find expressions for Vc(t) and Vr(t).

Homework Equations



Vc(t) = Vi * e(-t/rc)

The Attempt at a Solution



Vc(t) = 10e^(-100t)
Vr(t) = I have no clue and believe me I have spent a lot of time on this...
 
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  • #2
Hai, use kirchhoffs voltage law to find voltage across resistor
 

Related to Finding Voltage Across A Resistor in a 1st Order RC Circuit

1. What is a first order RC circuit?

A first order RC circuit is a type of electrical circuit that consists of a resistor (R) and a capacitor (C) connected in series. The resistor and capacitor form a voltage divider, which allows for the flow of current through the circuit. The first order refers to the fact that this type of circuit has only one energy storage element (the capacitor) and one energy dissipating element (the resistor).

2. How do I calculate the voltage across a resistor in a first order RC circuit?

The voltage across a resistor in a first order RC circuit can be calculated using Ohm's Law (V=IR). First, calculate the total resistance in the circuit by adding the resistance of the resistor (R) and the reactance of the capacitor (Xc = 1/2πfC). Then, multiply the total resistance by the current flowing through the circuit to get the voltage across the resistor.

3. What factors affect the voltage across a resistor in a first order RC circuit?

The voltage across a resistor in a first order RC circuit is affected by the resistance of the resistor, the capacitance of the capacitor, and the frequency of the input signal. A higher resistance or capacitance will result in a higher voltage, while a higher frequency will result in a lower voltage.

4. How does the voltage across a resistor change over time in a first order RC circuit?

The voltage across a resistor in a first order RC circuit decays over time as the capacitor charges up. Initially, the voltage across the resistor will be equal to the input voltage, but as the capacitor charges, the voltage will decrease. The rate at which the voltage decreases is determined by the time constant (T = RC) of the circuit.

5. Can the voltage across a resistor be negative in a first order RC circuit?

No, the voltage across a resistor cannot be negative in a first order RC circuit. The voltage across a resistor is always in the same direction as the current flowing through it. If the voltage across the resistor is negative, it would mean that the current is also flowing in the opposite direction, which is not possible in this type of circuit.

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