Shunt Resistance Calculation for a DC Circuit with 2 Parallel Resistors

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Discussion Overview

The discussion revolves around calculating the required value of a shunt resistance in a DC circuit with two parallel resistors, one being a meter with a known resistance and maximum current. Participants explore the relationships between current, voltage, and resistance in the context of this circuit.

Discussion Character

  • Homework-related, Mathematical reasoning, Technical explanation

Main Points Raised

  • Participants discuss the calculation of shunt current (Is) as Is = I - Im, where I is the total current and Im is the meter current.
  • There is a suggestion to maintain more decimal places for accuracy in calculations due to the difference between large and small currents.
  • One participant proposes using the formula V = IR to find the voltage across the meter resistance.
  • Another participant mentions using the product over sum rule to find voltage and questions how to rearrange it to solve for Rs.
  • There are multiple mentions of the importance of checking numerical values used in calculations, particularly for Im.
  • Participants discuss the concept of a current divider and its relevance to the problem, suggesting it could simplify the calculations.
  • There are corrections regarding the units used, with emphasis on distinguishing between current (mA) and voltage (mV).
  • Final calculations lead to a proposed value for Rs, with discussions on significant figures and scientific notation.

Areas of Agreement / Disagreement

Participants generally agree on the approach to calculating the shunt resistance, but there are disagreements on specific numerical values and the handling of units. The discussion remains somewhat unresolved regarding the best method to use for the calculations.

Contextual Notes

Participants note the importance of precision in calculations, particularly when dealing with small values in comparison to larger ones. There are also reminders to include units in results to avoid losing marks.

Who May Find This Useful

Students working on circuit analysis, particularly those studying parallel resistor configurations and shunt resistances in DC circuits.

damon669
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Homework Statement


DC circuit
2 resistors in parallel Rm and Rs
one resitance will be a meter (Rm =0.1 ohm), the other will be the shunt
Max current is 200A
Im (meter current is 1mA)



Homework Equations


I= Is + Im
V=IRt



The Attempt at a Solution


I am thinking first to find shunt current which Is
Is = I - Im
=199.9A ?
 
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damon669 said:

Homework Statement


DC circuit
2 resistors in parallel Rm and Rs
one resitance will be a meter (Rm =0.1 ohm), the other will be the shunt
Max current is 200A
Im (meter current is 1mA)



Homework Equations


I= Is + Im
V=IRt



The Attempt at a Solution


I am thinking first to find shunt current which Is
Is = I - Im
=199.9A ?

Hi damon669, Welcome to Physics Forums.

Yes, the shunt current will likely come in handy. What is it you're trying to find? Your problem description doesn't explicitly pose a question...
 
The question is
Determine the required value of the shunt resistance if the maximum value of the current I is 200A. The meter can read a maximum of 1 mA and has a resistance of 0.1Ω
 
damon669 said:
The question is
Determine the required value of the shunt resistance if the maximum value of the current I is 200A. The meter can read a maximum of 1 mA and has a resistance of 0.1Ω

Okay. So you know the currents that are flowing through each of the components (you might want to hang on to a few more decimal places for the shunt current for intermediate steps, since you are dealing with a difference between a large number and a tiny one). What else can you determine from the given values?
 
V=IR

so 0.1 x 0.00001
= 0.0000001
 
damon669 said:
V=IR

so 0.1 x 0.00001
= 0.0000001

Yes, you can determine the potential across the meter resistance. However, be careful of your decimal places... check the value you've used for current. (it's often advantageous to use scientific notation, particularly when metric prefixes are given). Also be sure to include units on results.

So then, what's the potential across the shunt resistance?
 
Rs = V/Is

10^(-6)/199.9
 
I read you can use product over sum rule to get V
V=I x RsRm/Rs+Rm
can I use this? if so how to make Rs the subject?
 
5mV?
 
  • #10
damon669 said:
Rs = V/Is

10^(-6)/199.9

Your result will be out by a few orders of magnitude. Did you check the current value that you used for I am as I suggested?
 
  • #11
damon669 said:
I read you can use product over sum rule to get V
V=I x RsRm/Rs+Rm
can I use this? if so how to make Rs the subject?

You could do that. It's just algebra, rearranging the expression. Start by getting rid of the fraction (multiply both sides by the denominator expression).

There's a more straightforward option, too. Look up "current divider". It would go well with the starting values you've been given.
 
  • #12
damon669 said:
5mV?

What is that supposed to be?
 
  • #13
current divider gives

I = I am + Is
so Is = I - I am (already done)
I - V/Rm
 
  • #14
gneill said:
What is that supposed to be?

thought i worked out the voltage to be 5mA, which would be the same in all parts of this parallel circuit
 
  • #15
damon669 said:
current divider gives

I = I am + Is
so Is = I - I am (already done)
I - V/Rm

That doesn't look like the current divider rule, and you're not given V ahead of time...

But before going on with a new method you need to fix the one you've used first. Check the numerical value you've used for Im!
 
  • #16
damon669 said:
thought i worked out the voltage to be 5mA, which would be the same in all parts of this parallel circuit

While it is true that the voltage will be the same across both resistances, that voltage is not 5mV !
(and mA is a current: milli-Amps).

Redo your voltage calculation and pay particular attention to the magnitudes of the values!
 
  • #17
V = IR
= 0.001 x 0.1
=0.0001
= 10^(-4)
 
  • #18
damon669 said:
V = IR
= 0.001 x 0.1
=0.0001
= 10^(-4)

That looks better :smile: Be sure to add units to your results! Always! You will lose marks if you fail to include units!

So, with an appropriate metric prefix that would be 0.1 mV.
 
  • #19
So Rs = V/Is
=0.0001/199.9
=0.0000005003 ohms
 
  • #20
damon669 said:
So Rs = V/Is
=0.0001/199.9
=0.0000005003 ohms

Yup. Now's the time to use scientific notation and round results to the appropriate number of significant figures.
 
  • #21
0.5003 microhms
 
  • #22
and that's it

must admit did not expect an microohm answer
 
  • #23
damon669 said:
0.5003 microhms
Too many significant figures... take a look at the original given values to determine how many significant figures are appropriate. Otherwise it looks good.
 
  • #24
0.5 microohm
 
  • #25
damon669 said:
0.5 microohm

Looks good! :approve:
 
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