- #1
teh_cookie
- 4
- 0
Homework Statement
Homework Equations
T = R*C
The Attempt at a Solution
I have no idea how to go about this. I know that T=R*C in a RC circuit
Time Constant RC circuit with dependent source
- Engineering
- Thread starter teh_cookie
- Start date
In summary, The time constant for this RC circuit can be found by finding the equivalent resistance of the resistor and dependent source, and multiplying it by the capacitance. Another method is to use the loop equation and differential equation relating Vc and Ic to find an exponential relation, and then solving for the time constant. Both methods should yield the same result.
T = R*C
I have no idea how to go about this. I know that T=R*C in a RC circuit
- #2
berkeman
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teh_cookie said:Homework Statement
Homework Equations
T = R*C
The Attempt at a Solution
I have no idea how to go about this. I know that T=R*C in a RC circuit
That time constant is true when you have a constant voltage source and you close a switch into the RC portion of the circuit (or similar setup). This problem looks different, since voltge source is depentent on the voltage drop through the resistor (and hence dependent on the current in the circuit).
I'd start with a loop equation for the loop, using the differential equation relating Vc and Ic. Then see if solving it gives an exponential relation still, and if it does, finding the time constant that results.
- #3
berkeman
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BTW, you're going to have to assume some initial condition to solve the problem, but since it's a linear circuit, the initial condition you choose shouldn't affect the time constant (at least I don't think it will).
- #4
Adjuster
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The combination of the resistor and the dependant source can be modeled as a resistance. Find this equivalent resistance by considering the capacitor replaced by a test current. Multiply the equivalent resistance by the capacitance of C to get the time constant.
- #5
berkeman
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Adjuster said:
Hah! Neat trick, and very logical. I hadn't seen that before.
But the OP should do it both ways, to check his answers...
- #6
CerealSteak
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Trying Adjuster's trick I basically get v_in=5*v_1, My guess is that I can translate that to a R_eq of 5. But 5*0.01 = 0.05s (an order of magnitude too small).
My guess is that I'm missing something here
edit: v_1 = 10 Ohms * i_in
v_in = 5 * (10 * i_in)
R_eq = 50 Ohms
50 Ohm * 0.01 F = 0.5 s
My guess is that I'm missing something here
edit: v_1 = 10 Ohms * i_in
v_in = 5 * (10 * i_in)
R_eq = 50 Ohms
50 Ohm * 0.01 F = 0.5 s
Last edited:
FAQ: Time Constant RC circuit with dependent source
1. What is a time constant in an RC circuit with a dependent source?
In an RC circuit with a dependent source, the time constant represents the time it takes for the voltage or current in the circuit to reach 63.2% of its maximum or steady state value. It is denoted by the symbol τ and is calculated by multiplying the resistance (R) and capacitance (C) values in the circuit.
2. How does a dependent source affect the time constant in an RC circuit?
A dependent source, also known as a controlled source, is a voltage or current source whose value is determined by the value of another voltage or current in the circuit. In an RC circuit, a dependent source can affect the time constant by changing the effective resistance or capacitance in the circuit. This means that the time constant will be different from the one calculated using the original resistance and capacitance values.
3. What is the relationship between the time constant and the charging/discharging of a capacitor in an RC circuit with a dependent source?
The time constant plays a crucial role in determining the rate at which a capacitor charges or discharges in an RC circuit with a dependent source. A larger time constant means that the capacitor will take longer to charge or discharge, while a smaller time constant results in a faster charging or discharging process.
4. How can the time constant be adjusted in an RC circuit with a dependent source?
The time constant in an RC circuit with a dependent source can be adjusted by varying the values of the dependent source, resistance, or capacitance in the circuit. This can be done by using different components or by changing the circuit configuration.
5. What are some practical applications of RC circuits with dependent sources and time constants?
RC circuits with dependent sources and time constants have various applications in electronics, such as in filters, oscillators, and timers. They are also commonly used in electronic devices, such as radios, televisions, and computers, to process and control signals. Additionally, these circuits are essential in the design and functioning of power supplies and battery charging circuits.
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