Circuit with resistors in series and two power supplies

[743344]

Homework Statement

There is a current of 0.25 A in the circuit of the figure

What is the value of the resistance R?

Homework Equations

V = IR

The Attempt at a Solution

since the circuit is in series:

V = 6+ 12 = 18V
Req = R + 6 + 12
V = IReq
Req = 18/0.25 = 72

72 = 18+ R
R = 54

but the answer is wrong !
help

 

[Oerg]

is the answer 30?

 

[mysqlpress]

current of the whole circuit =0.25A

I=V/R = (12-6)/(18+R) = 6/(18+R)
4.5+0.25R=6
0.25R=1.5
R=6 ?
I am not sure ...

 

[Mike Cookson]

I'm sure you know Kirchoff's voltage law - "The sum of all voltage drops around any closed loop must be equal to zero.

Applying Kirchoff's voltage law gives ->
0 = Power supply driving current (largest voltage) - Power supply opposing flow of current (smallest voltage) - Voltage drop across resistance in circuit (6Ohm, 12Ohm and ROhm).

0 = 12 - 6 -(6*0.25) - (12*0.25) - 0.25R
Thus..
0 = 6 - 1.5 - 3 - 0.25R
So..
0= 1.5 - 0.25R
0.25R = 1.5
R = 6Ohms

 

[physixguru]

Ohm's law is something in this world i guess...

 

[physixguru]

Ohm's law is something i guess.

 

[Mike Cookson]

Ohms law is something - but in this case Kirchoff's voltage law is something also.

 

[physixguru]

Utility of the either one counts.

 

[Oerg]

My take on this is that because there is a charge flow from the 12V battery and the potential of this battery is higher than the 6V, the 6V does not release any electrons at all and acts as a conductor.

 

[geleem]

the circuit is an illusion.

the effective voltage is not 18 volts, it is 6 volts.

redrawing circuit with resistors in one leg and batteries
in another gives a better understanding of actual circuit.

6 ohm 12 ohm Rx
+----VVVV----VVVV----VVVV---+
| |
__|__ + | E/I = Rt
___ 12 V | 6V/.25A = 24 OHM total
_____ | therefore;
___ | 6 + 12 + Rx = 24 OHM
| | Rx = 6 OHM
| 6 volts effective |
_|_ |
_____ |
___ |
_____ 6 V |
| + |
| |
+-------------------------------------+

 

[geleem]

please excuse previous post. seems that character graphics can not be used on this forum.

repeating text of previous post and adding a graphic to show redrawn circuit.

++++
the circuit is an illusion.

when 2 batteries connected with like polarities connected cause lesser voltage to be subtracted
from higher voltage. therefore, the effective voltage is not 6 volts + 12 volts = 18 volts.

it is 12 volts - 6 volts = 6 volts.


attached redrawing of circuit with resistors in one leg and batteries in another leg
gives a better of what is actual circuit.

using formula,
E/I = Rt
6V/.25A = 24 OHM total
therefore;
6 + 12 + Rx = 24 OHM
Rx = 6 OHM

 

[mikelepore]

when 2 batteries connected with like polarities connected cause lesser voltage to be subtracted
from higher voltage. therefore, the effective voltage is not 6 volts + 12 volts = 18 volts.

it is 12 volts - 6 volts = 6 volts.

You are right. A person should go around the loop in one direction, say, arbitrarily choosing clockwise. Then we would encounter one battery in the polarity plus-minus and we would encounter the other battery in the polarity minus-plus. Therefore the batteries oppose one another. We have to subtract the batteries, not add them.

 

[geleem]

A person should go around the loop in one direction, say, arbitrarily choosing clockwise.

this is true. considering as a loop is one way to look at it.

when i first looked at circuit, i saw reason "743344"'s formula did not work just from fact being that
'load' side, [normal of convention of supply to left, load to right of a circuit] had an opposing voltage.

"mysqlpress" replied with correct answer in formula without a corrected drawing.

"Mike Cookson" replied with an implication of "Kirchoff's voltage law", no drawing.

24 Dec 2009, 06:48 PM UTC, i attempted an 'ascii graphic' of circuit, which failed due to
compressing of spaces used.

after seeing this, i submitted again, 24 Dec 2009, 07:46 PM UTC, with an 'attached' drawing,
which for some reason or other, did not get shown. [i just now tried an edit and was able to get
attachment to save]

all in all, another way to spend December 24th UTC.

happy Christmas to all.