Shunt Resistance Calculation for a DC Circuit with 2 Parallel Resistors

[damon669]

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 ?

 

[gneill]

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...

 

[damon669]

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

 

[gneill]

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?

 

[damon669]

V=IR

so 0.1 x 0.00001
= 0.0000001

 

[gneill]

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?

 

[damon669]

Rs = V/Is

10^(-6)/199.9

 

[damon669]

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?

 

[damon669]

5mV?

 

[gneill]

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?

 

[gneill]

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.

 

[gneill]

5mV?

What is that supposed to be?

 

[damon669]

current divider gives

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

 

[damon669]

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

 

[gneill]

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!

 

[gneill]

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!

 

[damon669]

V = IR
= 0.001 x 0.1
=0.0001
= 10^(-4)

 

[gneill]

V = IR
= 0.001 x 0.1
=0.0001
= 10^(-4)

That looks better 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.

 

[damon669]

So Rs = V/Is
=0.0001/199.9
=0.0000005003 ohms

 

[gneill]

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.

 

[damon669]

0.5003 microhms

 

[damon669]

and that's it

must admit did not expect an microohm answer

 

[gneill]

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.

 

[damon669]

0.5 microohm

 

[gneill]

0.5 microohm

Looks good!