How Do You Calculate Total Resistance in Mixed Resistor Circuits?

[shihab-kol]

Homework Statement

2. Homework Equations [/B]
$V = IR$

The Attempt at a Solution

My solution:
R1,R2,R3 are in parallel and so we can find their total R

$\frac {R1×R2×R3}{R1+R2+R3} = R'$

$R' = \frac {10}{3}$
R' is in series with R4

$∴ R= R' + R4 = \frac{10}{3} +10 = \frac{40}{3}\Omega$

We find current to be ,
$$I=\frac{3}{4} A ------(From ~Ohm's~ Law)$$
$V ~across~ R1,R2,R3 ~is~ same ~and ~I~ across ~R'~ and ~R ~is ~same$

$$∴ V'=I×R'=\frac{3}{4}×\frac{10}{3}=\frac {5}{2}$$

Similarly, we find for the other.

Is my process alright ?

 

[lewando]

R1,R2,R3 are in parallel...

Are they? Review the definition of circuit elements in parallel.

 

[shihab-kol]

Are they? Review the definition of circuit elements in parallel.

Is it that R2,R3 Are in parallel and R1 is not?

 

[cnh1995]

R1,R2,R3 are in parallel and so we can find their total R

Remove the voltmeters and trace the path of current from A to B. What can you say about the current through the resistors?

R1×R2×R3R1+R2+R3=R′R1×R2×R3R1+R2+R3=R′ \frac {R1×R2×R3}{R1+R2+R3} = R'

Even if the resistors were in parallel, this formula is incorrect. It has the dimensions of R² and not R.

 

[shihab-kol]

Remove the voltmeters and trace the path of current from A to B. What can you say about the current through the resistors?Even if the resistors were in parallel, this formula is incorrect. It has the dimensions of R² and not R.

Removing voltmeters and included wires it is a series combo.
I couldn't understand the second part .

 

[cnh1995]

Removing voltmeters and included wires it is a series combo.

Yes.
(But just remove the voltmeters. Don't replace them with wires. This is because ideal voltmeters don't draw any current i.e. they act as open circuits. )

I couldn't understand the second part .

The formula you used is incorrect. Look up the correct formula. (Not for this problem of course).

So if the resistors are in series, what will each voltmeter read?

 

[andrevdh]

maybe it will be clearer if you draw the series connection of the four resistors in one straight line and then connect the voltmeters over the various parts of the circuits?

 

[andrevdh]

What would the potential difference be over each of the resistors since they are in series with each other?
a voltmeter has a very high resistance so you could ignore them, they do not alter or influence the resistor circuit in any way.

 

[shihab-kol]

I have not thought about it but on its face since resistance is same as well as current each well have the same reading.

 

[phinds]

I have not thought about it but on its face since resistance is same as well as current each well have the same reading.

Really? Does #4 read the same as the rest? What voltage does #2 read? I suggest you redraw the circuit and rethink your answer.

 

[andrevdh]

yes, the potential difference over each resistor will be the same. what should it be?

 

[phinds]

yes, the potential difference over each resistor will be the same. what should it be?

I said NOTHING about the potential resistance over each resistor. My comment was about what the voltmeters will read.

 

[andrevdh]

sorry, yes, I was communicating with shihab-kol

 

[phinds]

sorry, yes, I was communicating with shihab-kol

To avoid such confusion, use the quote button so everyone know what post you are responding to.

 

[andrevdh]

will do