Electromagnetism Current Curcuits

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SUMMARY

The discussion focuses on analyzing a circuit with four resistors connected to a battery, specifically examining the potential differences and currents through each resistor. The resistors are defined as R1 = R, R2 = 2R, R3 = 4R, and R4 = 3R. The correct rankings for potential differences are R2 < R1 < R3 < R4, while the current rankings are I1 > I4 > I2 = I3. When R3 is increased, I4 increases while I1, I2, and I3 decrease. In the limit where R3 approaches infinity, I2 and I3 become zero, while I1 remains I, indicating a change in current distribution.

PREREQUISITES
  • Understanding of Ohm's Law and Kirchhoff's circuit laws
  • Familiarity with series and parallel resistor configurations
  • Knowledge of electromotive force (emf) and its role in circuits
  • Basic algebra for manipulating equations related to electrical circuits
NEXT STEPS
  • Study the effects of varying resistor values on circuit behavior using simulation tools like LTspice
  • Learn about the concept of equivalent resistance in complex circuits
  • Explore the implications of increasing resistance on current flow in circuits
  • Investigate the relationship between voltage, current, and resistance in AC circuits
USEFUL FOR

Electrical engineering students, circuit designers, and anyone interested in understanding the principles of electromagnetism and current flow in electrical circuits.

JJBrian
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Four resistors are connected to a battery as shown in the figure. The current in the battery is I, the battery emf is emf, and the resistor values are R1 = R, R2 = 2R, R3 = 4R, and R4 = 3R.

Picture:
http://www.webassign.net/serpop/p21-32.gif


(a) Rank the resistors according to the potential difference across them, from largest to smallest. (Use the form R1 for R1.)
R2<R1<R3<R4 (Correct)

(b) Determine the potential difference across each resistor in terms of emf. (Use E for emf, as necessary.)
ΔV1 = E/3 Answer is correct.
ΔV2 = 2E9 Answer is correct.
ΔV3 = 4E/9 Answer is correct.
ΔV4 = 2E/3 Answer is correct.

(c) Rank the resistors according to the current in them, from largest to smallest. Note any cases of equal currents.
I1 > I4 > I2 = I3 Answer is correct.

(d) Determine the current in each resistor in terms of I. (Use I, as necessary.)
I1 = I. Your answer is correct.
I2 = I/3. Your answer is correct.
I3 = I/3 Your answer is correct.
I4 = 2I/3 Your answer is correct.

(e) If R3 is increased, what happens to the current in each of the resistors?

I4 increases and I1, I2, and I3 decrease. Your answer is correct.


(f) In the limit that R3 → infinity, what are the new values of the current in each resistor in terms of I, the original current in the battery? (Use I, as necessary.)
I1 = I Your answer is incorrect.
I2 = 0. Your answer is correct.
I3 = 0. Your answer is correct.
I4 = I. Your answer is incorrect.

I would like some help on part (f).
 
Last edited:
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You are correct .
 

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