What happens to the total power dissipated in the circuit ?

Click For Summary
SUMMARY

The total power dissipated in a circuit remains constant when a switch is closed, despite changes in current distribution. When the switch is closed, the equivalent resistance (Req) decreases due to the parallel configuration of components, leading to an increase in total current (Itotal). The voltage across components A and B increases as the voltage across component C decreases, maintaining the total voltage equal to the battery voltage. This analysis relies on the principles of current conservation and Ohm's law, specifically the equations Pr=Pbat=dEth/dt=(dq/dt)*Vr=I*Vr.

PREREQUISITES
  • Understanding of Ohm's Law (I=V/R)
  • Knowledge of series and parallel circuit configurations
  • Familiarity with the concept of equivalent resistance (Req)
  • Basic principles of electrical power (Pr=Pbat)
NEXT STEPS
  • Study the effects of short circuits on circuit behavior
  • Learn about Kirchhoff's laws for current and voltage in circuits
  • Explore the concept of power dissipation in resistive circuits
  • Investigate the implications of changing circuit configurations on total resistance
USEFUL FOR

Students studying electrical engineering, physics enthusiasts, and anyone seeking to understand circuit behavior in relation to power dissipation and resistance changes.

kamhogo
Messages
86
Reaction score
6

Homework Statement


What happens to the total power dissipated in the circuit once the switch is closed?
tmp_3989-20160409_2113301282769602.jpg

Homework Equations


Pr=Pbat=dEth/dt=(dq/dt)*Vr=I*Vr[/B]

The Attempt at a Solution


V total and I toral remain the same so the power dissipated by the circuit stays the same...?
 
Physics news on Phys.org
Why do you think Itotal remains the same? What is the resistance across the battery with the switch open and with it closed?
 
Can you show some equations to back up your guess?
 
phyzguy said:
Why do you think Itotal remains the same? What is the resistance across the battery with the switch open and with it closed?

Well...for the current, it's current conservation. Switch open: I total goes through A, B and C ( they're in series) and then goes back to the battery. Switch closed: I total goes through A then B then splits into let's say I1( through the middle resustless wire) and I2 ( through C) at the upper junction. Then it becomes I total again at the lower junction. I think the closed switch short-circuits C but I am not sure this means I2 is null...As for the voltages, I think the voltage across C has to decrease once the switch is closed ( V=IR, I decreases; V decreases). But the total voltage has to stay the same ( equal to the voltage provided by the battery) so the voltages across A and B have to increase...but that would mean that the current through A and B increases...?!?
 
gneill said:
Can you show some equations to back up your guess?
Pr=Pbat=dEth/dt=(dq/dt)*Vr=I*Vr
I got his from my textbook. We haven't learned it in class yet, so I am confused about it and the textbook does not help..
 
What happens to the total resistance of the circuit when the switch is closed?
 
kamhogo said:
But the total voltage has to stay the same ( equal to the voltage provided by the battery) so the voltages across A and B have to increase...but that would mean that the current through A and B increases...?!?
Right.
 
cnh1995 said:
Right.
But how is that possible? A and B are right after the positive terminal of the battery so no matter the situation they should receive I total...?
 
kamhogo said:
But how is that possible? A and B are right after the positive terminal of the battery so no matter the situation they should receive I total...?
cnh1995 said:
What happens to the total resistance of the circuit when the switch is closed?
 
  • #10
kamhogo said:
But how is that possible? A and B are right after the positive terminal of the battery so no matter the situation they should receive I total...?

Of course A and B receive all of Itotal, but Itotal is different when the switch is closed than when it is open.
 
  • #11
l think I see. Itotal=Vtotal*Req. Switch open: Req =3R (the bulbs are identical and in series). Switch closed: Req is smaller than 3R (C is now in parallel with A and B). So I is smaller when the switch is closed. Correct?
 

Attachments

  • upload_2016-4-10_1-49-35.png
    upload_2016-4-10_1-49-35.png
    56.5 KB · Views: 739
  • #12
kamhogo said:
Switch closed: Req is smaller than 3R
Yes.
kamhogo said:
C is now in parallel with A and B).
No. C is eliminated from the circuit. Look up the term "short circuit".
kamhogo said:
So I is smaller when the switch is closed.
Are you sure? Equivalent resistance decreased after closing the switch.
 
  • #13
kamhogo said:
Itotal=Vtotal*Req.
I=V/R and not V*R.
 
  • #14
cnh1995 said:
I=V/R and not V*R.
True! So the current increases.
 

Similar threads

Power dissipated in this circuit with 2 batteries and 3 resistors
  • · Replies 22 ·
Replies
22
Views
4K
How Does Power Dissipation in One Resistor Relate to Total Power from Batteries?
  • · Replies 1 ·
Replies
1
Views
2K
How Much Energy is Dissipated in a Resistor in 0.75 Seconds?
  • · Replies 3 ·
Replies
3
Views
2K
Power Resistor Immersed In Water
  • · Replies 4 ·
Replies
4
Views
3K
Untangling a Confusing Circuit: Solving Kirchoff's DC Laws
  • · Replies 12 ·
Replies
12
Views
1K
Circuit analysis: Six resistors and two batteries
  • · Replies 1 ·
Replies
1
Views
2K
What is the Mistake in Calculating Power Dissipation in a Resistor?
  • · Replies 10 ·
Replies
10
Views
2K
Average power dissipation for induced current
  • · Replies 2 ·
Replies
2
Views
3K
Power Dissipated By Resistor is LRC Circuit
  • · Replies 3 ·
Replies
3
Views
4K
Resistors (lightbulbs) Power & Brightness
  • · Replies 13 ·
Replies
13
Views
3K