Linear circuit analysis question

In summary, at 12 volts, the power at the top and bottom resistors must be 0 in order for the resistor not to dissipate power.
  • #1
arkturus
27
0

Homework Statement



Replace resistor R with a voltage source such that no power is absorbed by either resistor; draw the circuit, indicating the voltage polarity of the new source.

circuit.jpg


Homework Equations



Ohm's law, Power = IV = I^2 * R

The Attempt at a Solution



I'm honestly not too sure how to begin the problem. The total voltage across the circuit should add up to zero, so I'm guessing the new voltage source must be 12V, but that seems too simple.

Thanks for the help.
 
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  • #2
What must the voltage be across a resistor in order for that resistor not to dissipate power? What would the voltage of a voltage source at R be in order to achieve that condition?

E.g., start with the 15 k resistor at the top. What would the voltage have to be at the top of R in order for the 15k resistor not to dissipate power?
 
  • #3
skeptic2 said:
What must the voltage be across a resistor in order for that resistor not to dissipate power? What would the voltage of a voltage source at R be in order to achieve that condition?

E.g., start with the 15 k resistor at the top. What would the voltage have to be at the top of R in order for the 15k resistor not to dissipate power?

I'm honestly not sure what the voltage must be through a resistor in order for it to not dissipate power. Is there a relationship I'm missing?
 
  • #4
What is the formula for power dissipated by a resistor in terms of voltage?
 
  • #5
skeptic2 said:
What is the formula for power dissipated by a resistor in terms of voltage?

Ah, got it. I was thinking in terms of P = I*V, but P = V^2/R works too.

I think my issue with the problem is the phrasing of "dissipating power". Does that mean that power will be zero?

I'm assuming the voltages would have to be 0 in order for power to be zero.
 
  • #6
That's right, power is zero when the voltage is zero. What voltage would a voltage source at R have to be to get zero volts across the resistors?
 
  • #7
skeptic2 said:
That's right, power is zero when the voltage is zero. What voltage would a voltage source at R have to be to get zero volts across the resistors?

Ah I got it, R should be replace with +12 volts. That way there is a net voltage of 0 throughout the circuit thus power at the top and bottom resistors must be 0?
 
  • #8
Very good.
 
  • #9
Thanks a lot, you were a big help
 

1. What is linear circuit analysis?

Linear circuit analysis is a method used to analyze the behavior and characteristics of electrical circuits composed of linear components, such as resistors, capacitors, and inductors. It involves solving mathematical equations and using circuit laws to determine the voltage, current, and power in a circuit.

2. What are the basic principles of linear circuit analysis?

The basic principles of linear circuit analysis include Ohm's Law, Kirchhoff's Laws, and the principle of superposition. Ohm's Law states that the current through a conductor is directly proportional to the voltage and inversely proportional to the resistance. Kirchhoff's Laws state that the sum of currents entering a node must equal the sum of currents leaving the node, and the sum of voltages around a closed loop must equal zero. The principle of superposition states that the total response of a circuit is the sum of the individual responses to each input.

3. What are the main techniques used in linear circuit analysis?

The main techniques used in linear circuit analysis are nodal analysis, mesh analysis, and the use of equivalent circuits. Nodal analysis involves writing equations at each node to determine the unknown node voltages. Mesh analysis involves writing equations for each loop in the circuit to determine the unknown currents. Equivalent circuits involve simplifying a complex circuit into an equivalent circuit with a single voltage source and a single impedance.

4. What are the limitations of linear circuit analysis?

Linear circuit analysis is only applicable to circuits with linear components. It also assumes that the circuit operates at a single frequency or over a narrow range of frequencies. Nonlinear components, such as diodes and transistors, cannot be accurately analyzed using linear circuit analysis. Additionally, parasitic elements, such as stray capacitance and inductance, can affect the accuracy of the analysis.

5. What are some real-world applications of linear circuit analysis?

Linear circuit analysis is used in a wide range of applications, including electronic devices, power systems, and communication systems. It is essential for designing and analyzing circuits in computers, smartphones, and other electronic devices. It is also used in power grids to ensure efficient and stable distribution of electricity. In communication systems, linear circuit analysis is used to analyze and design filters, amplifiers, and other components.

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