What is the voltage in a parallel circuit?

AI Thread Summary
In a parallel circuit, the potentials at points E, F, A, and B are equal due to the absence of resistance, leading to the conclusion that voltage across each resistor is the same. Despite differences in potential energy losses across resistors R1 and R2, the voltage drop remains consistent, as indicated by the equal potentials at points C and G. The currents I1 and I2 adjust to maintain equal voltage drops across the resistors. While potential energy lost differs between resistors, the potential energy lost per charge remains constant, confirming that the potentials at points C and G are equal. Therefore, the voltage in a parallel circuit is uniform across all branches.
erocored
Messages
30
Reaction score
7
Potentials in points E, F, A, B are equal because there is no resistance. In my opinion, losses of potential energy in the resitors R1 and R2 are not equal (potential C ≠ potential G). Then why do we say that voltage in this circuit is the same?
 

Attachments

  • 2.png
    2.png
    4.1 KB · Views: 188
Physics news on Phys.org
Why not? Like you said, ##\phi_A = \phi_B = \phi_E = \phi_F##, and likewise ##\phi_C = \phi_D = \phi_G = \phi_H##. Then ##V_{BC} = \phi_B - \phi_C##, and ##V_{FG} = \phi_F - \phi_G##, and so ##V_{BC} = V_{FG}##.

You might say that the voltages across each resistor, which are the differences in potential energy of a unit charge on either end of the resistor, are equal.
 
  • Like
Likes Dale
etotheipi said:
Why not? Like you said, ##\phi_A = \phi_B = \phi_E = \phi_F##, and likewise ##\phi_C = \phi_D = \phi_G = \phi_H##. Then ##V_{BC} = \phi_B - \phi_C##, and ##V_{FG} = \phi_F - \phi_G##, and so ##V_{BC} = V_{FG}##.

You might say that the voltages across each resistor, which are the differences in potential energy of a unit charge on either end of the resistor, are equal.
Is it possible that potential C > potential G?
 
erocored said:
Is it possible that potential C > potential G?

Not in your diagram, no. Just look at the path ##C \rightarrow D \rightarrow H \rightarrow G##. Each of those 3 wires have zero resistance, so have zero voltage across them.
 
  • Like
Likes Delta2 and erocored
The fact that the voltages C and G are equal is what you use to determine the two currents I1 and I2. You could say the currents "adjust themselves" to achieve the same voltage drops.
 
  • Like
Likes russ_watters, Delta2 and erocored
erocored said:
In my opinion, losses of potential energy in the resitors R1 and R2 are not equal (potential C ≠ potential G).
The statement outside of the parentheses is true, and the statement in the parentheses is false. Remember that potential is not equal to potential energy but rather is equal to potential energy per charge.

Yes, the potential energy lost is different in the two resistors, but so is the amount of charge passing the two resistors. The potential energy lost per charge is the same. So the potential at C is equal to the potential at G.
 
  • Like
Likes Lord Jestocost, erocored, nasu and 1 other person
Susskind (in The Theoretical Minimum, volume 1, pages 203-205) writes the Lagrangian for the magnetic field as ##L=\frac m 2(\dot x^2+\dot y^2 + \dot z^2)+ \frac e c (\dot x A_x +\dot y A_y +\dot z A_z)## and then calculates ##\dot p_x =ma_x + \frac e c \frac d {dt} A_x=ma_x + \frac e c(\frac {\partial A_x} {\partial x}\dot x + \frac {\partial A_x} {\partial y}\dot y + \frac {\partial A_x} {\partial z}\dot z)##. I have problems with the last step. I might have written ##\frac {dA_x} {dt}...
Thread 'Griffith, Electrodynamics, 4th Edition, Example 4.8. (Second part)'
I am reading the Griffith, Electrodynamics book, 4th edition, Example 4.8. I want to understand some issues more correctly. It's a little bit difficult to understand now. > Example 4.8. Suppose the entire region below the plane ##z=0## in Fig. 4.28 is filled with uniform linear dielectric material of susceptibility ##\chi_e##. Calculate the force on a point charge ##q## situated a distance ##d## above the origin. In the page 196, in the first paragraph, the author argues as follows ...
Back
Top