Will there be a difference between the readings of V1 and V2

[prakhargupta3301]

I= Current flowing
V₁= Voltmeter 1
V₂= Voltmeter 2

My question is that if there would be any difference between the readings of V₁ and V₂?
We know that: By Ohm's law: V= I.R
also:
Combined resistance of R₁ and R₂ will be:
1/R_{Combined Resistance of R1 and R2}= 1/R₁+1/R₂
The reading in V₂ will be : (V₂= I. Combined resistance of R₁ and R₂)
But the current flowing in the circuit will get divided into two unknown parts at point C.
Now, if the current I is being divided, then the reading of V₁ should be different than V₂.
This is my problem please guide me.
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[magoo]

No. They will both give you a measurement equivalent to connecting the voltmeter between C and D.

 

[rude man]

Lines on a schematic diagram are considered equipotentials. That ought to answer your question ipso facto.

 

[haruspex]

the current flowing in the circuit will get divided into two unknown parts at point C.

You can determine the ratio from the fact that the potential is the same, which means that...

if the current I is being divided, then the reading of V1 should be different than V2.

... no, it is divided in just such a way that V1and V2 are the same.

 

[scottdave]

If you calculate the value of current (I) delivered by the battery cell, this value will be split so that a certain portion goes through r1, and the rest of the current goes through r2. The voltage measurements as you have configured will be practically the same, since the resistance of the wire is very low, compared to the components in the circuit.
Refer to this table of wire resistances for typical sizes of copper wiring. If you are using 20 gauge wire, it will take 1000 feet of wire to result in 10 ohms of resistance. http://hyperphysics.phy-astr.gsu.edu/hbase/Tables/wirega.html

 

[CWatters]

Another way of looking at it is to consider the length of the of wires. The length of A-C, C-E, B-D & D-F are not specified so they could have zero length. This would mean A and E are in the same physical and electrical place, B and F likewise. Then it's obvious V1 and V2 must be the same.