Linear circuit analysis question

Click For Summary
SUMMARY

The discussion centers on replacing a resistor (R) with a voltage source to ensure that no power is absorbed by either resistor in a linear circuit. The key conclusion is that the voltage source should be +12V, which results in a net voltage of 0 across the circuit, thereby preventing power dissipation in the resistors. The relevant equations discussed include Ohm's Law and the power formulas P = IV and P = V²/R, which clarify the conditions under which power dissipation occurs.

PREREQUISITES
  • Understanding of Ohm's Law
  • Familiarity with power formulas: P = IV and P = V²/R
  • Basic knowledge of circuit analysis
  • Ability to interpret voltage sources and their effects on circuit behavior
NEXT STEPS
  • Study the concept of power dissipation in resistors
  • Learn about circuit analysis techniques using Kirchhoff's laws
  • Explore the implications of voltage sources in circuit design
  • Investigate the behavior of series and parallel resistor configurations
USEFUL FOR

Electrical engineering students, circuit designers, and anyone involved in analyzing or designing linear circuits will benefit from this discussion.

arkturus
Messages
27
Reaction score
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.
 
Last edited:
Physics news on Phys.org
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?
 
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?
 
What is the formula for power dissipated by a resistor in terms of voltage?
 
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.
 
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?
 
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?
 
Very good.
 
Thanks a lot, you were a big help
 

Similar threads

Engineering Why is the voltage source high potential into node 1 at -12 V in this op amp problem?
  • · Replies 15 ·
Replies
15
Views
2K
Engineering Why Is Nodal Analysis Confusing in This Circuit Example?
  • · Replies 7 ·
Replies
7
Views
2K
Engineering Question on basic circuit analysis
  • · Replies 4 ·
Replies
4
Views
2K
Engineering Create a circuit in simulation to prove my work (2 batteries and 1 lamp bulb)
  • · Replies 5 ·
Replies
5
Views
2K
Engineering Understanding the output waveform and using LTSpice
  • · Replies 1 ·
Replies
1
Views
2K
Engineering Norton/Thevenin Equivalent circuits with a dependent voltage source
  • · Replies 9 ·
Replies
9
Views
6K
Engineering Finding the Thevenin Equivalent Circuit for a Network with a Load Resistor
  • · Replies 1 ·
Replies
1
Views
2K
Engineering Step response of RC circuit with independent voltage and current sources
  • · Replies 7 ·
Replies
7
Views
3K
Engineering Unknown resistor in a series-parallel circuit
  • · Replies 17 ·
Replies
17
Views
13K
Engineering Can a voltage test source help solve for Rth in a complex Thevenin's circuit?
  • · Replies 10 ·
Replies
10
Views
2K