Looks simple at first but really found it difficult.

  • Thread starter Thread starter maobadi
  • Start date Start date
Click For Summary

Discussion Overview

The discussion revolves around determining the resistances of two resistors, Ra and Rb, connected in series with a battery. Participants explore the relationships between voltage readings across the resistors and the effect of a voltmeter's resistance on these readings. The scope includes mathematical reasoning and problem-solving related to circuit analysis.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant states that Ra has a lower resistance than Rb and prompts others to show their work.
  • Another participant asks if the formula for parallel resistance is known and suggests rearranging it to find Ra if Rp and Rm are known.
  • Several participants provide equations based on the voltage readings and the resistances, indicating the need to consider different currents for each measurement scenario.
  • A participant points out a mistake in assuming the battery current is the same in both cases and suggests rewriting the equations to reflect different currents (i1 and i2).
  • Another participant outlines a method to eliminate currents between equations to solve for Ra and Rb.
  • Additional equations are presented to express the voltages across the resistors and the meter, along with the relationships for currents through the meter when measuring each resistor.

Areas of Agreement / Disagreement

Participants generally agree on the need to derive equations based on the given voltages and resistances, but there is no consensus on the specific approach to take or the correctness of the initial assumptions regarding current.

Contextual Notes

There are unresolved mathematical steps and dependencies on the definitions of voltage and current in the context of the circuit. The discussion reflects varying levels of understanding and approaches to the problem.

maobadi
Messages
22
Reaction score
0
Two resistors Ra and Rb are connected in series with each other between the terminals of a battery giving a constant pd of 49V. When a voltmeter of 500 ohm resistance is connected across each in turn, the reading are given as Va = 14V and Vb = 28V. Determine the resistance of Ra and Rb..
 
Physics news on Phys.org
I'll give you this much: Ra has a lower resistance than Rb. You are going to have to show some work here. What have you determined so far? It's basic algebra which I hate to admit I'm a bit rusty at right now. This should be moved to homework section.
 
Do you know the formula to find the parallel resistance (Rp) of Ra and the meter (Rm)? If so, can you rearrange it to find Ra if you know Rp and Rm?
 
((500Ra)/(Ra+500))i = 14
((500Rb)/(Rb+500))i = 28

(Ra+Rb)i = 49

This what I have come up with but where do I go from here
 
maobadi said:
((500Ra)/(Ra+500))i = 14
((500Rb)/(Rb+500))i = 28

(Ra+Rb)i = 49

This what I have come up with but where do I go from here

Your first mistake is in assuming the battery current is the same in the two cases. You need to rewrite your equations as:

((500Ra)/(Ra+500))i1 = 14
((500Rb)/(Rb+500))i2 = 28

You also know that:

((500Ra)/(Ra+500))i1 + Rb*i1 = 49
((500Rb)/(Rb+500))i2 + Ra*i2 = 49

You can eliminate I1 between the the first two equations of each pair, and I2 between the second two of each pair.

This will give you two equations in the two unknowns, Ra and Rb. You should be able to proceed from there.
 
Given:
Vs = 49
Va = 14
Vb = 28
Rm = 500 meter resistance

V(Ra) = Vs - Vb
V(Ra) is the voltage across Ra when the meter is across Rb

V(Rb) = Vs - Va

V(Rm) = V(Rp)*V(Ra)/(V(Ra) - V(Rp))
V(Rm) is the voltage across the meter if Ra
were removed and just the meter were in
series with Rb.

Ia = Va(Rm)/Rm
Ia is current through the meter when it is
replacing Ra.

Ib = Vb(Rm)/Rm
Ib is current through the meter when it is
replacing Rb.

Ra = V(Ra)/Ia
Rb = V(Rb)/Ib
 
Last edited:

Similar threads

Engineering Electric Circuits Delta-to-Y and Y-to-Delta Transformation
  • · Replies 1 ·
Replies
1
Views
5K
How to find the relative error in the voltage reading
  • · Replies 9 ·
Replies
9
Views
7K
Ammeter and voltmeter resistance
  • · Replies 6 ·
Replies
6
Views
12K
Why Do Voltmeter Readings Differ in a Series Circuit?
  • · Replies 3 ·
Replies
3
Views
2K
Engineering Simple circuit - Finding Equivalent Resistance
  • · Replies 2 ·
Replies
2
Views
4K
Why do the headlights on the car become dim when the car is starting?
  • · Replies 4 ·
Replies
4
Views
2K
Relay Control of Induction Motors
  • · Replies 5 ·
Replies
5
Views
2K
Electricity - Series and Parallel Circuit
  • · Replies 3 ·
Replies
3
Views
6K
Voltmeter problem from (OCR paper) multiple choice
  • · Replies 7 ·
Replies
7
Views
2K
Unraveling the Mystery of EMF Internal Resistance
  • · Replies 2 ·
Replies
2
Views
2K