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3 resistors 4 ohm,6 ohm and 12 ohm are connected in parallel.The combination of the above resistors is connected in series to a resistance of 2 ohm and then to a battery of 6 volt. draw a circuit diagram and calculate: a)current in the main circuit. b)current flowing through each of the resistors in parallel. c)potential difference across the 2 ohm resistor. (diagram is not necessary).

3 resistors 4 ohm,6 ohm and 12 ohm are connected in parallel.The combination of the above resistors is connected in series to a resistance of 2 ohm and then to a battery of 6 volt. draw a circuit diagram and calculate:
a)current in the main circuit.
b)current flowing through each of the resistors in parallel.
c)potential difference across the 2 ohm resistor.
(diagram is not necessary).

Grade:10

5 Answers

Aarti Gupta
askIITians Faculty 300 Points
6 years ago
Given-
R1 = 4ohm
R2 = 6ohm
R3 = 12ohm
Rs = 2ohm (Series resistor)
Potential difference,V = 6V
Let the resistance of all three resistors which are connected in parallel be Rp
Then,
1/Rp = 1/R1 +1/R2 + 1/R3
1/Rp = 1/4 + 1/6 + 1/12
1/Rp = 6/12
or,Rp = 12/6 = 2ohm
Let total resistance be Rt = Rp +Rs
Rt = 2 + 2 = 4ohm
a).So current,I in the main circuit will be V=IR
therefore, I = V/R = 6/4 = 1.5A which is total current.
b) Since in parallel the current will divided into three resistors connected in parallel.Let the current across all the three be I1,I2 and I3.
Now,
I1 = V/R1 (Since potential difference is same as they are connected in parallel)
I1 = 6/4 = 1.5A
Similarly,I2 = V/R2
I2 = 6/6 = 1A
and I3 = 6/12 = 0.5A
c). V across 2ohm resistor will be-
V = I*R ( I will be total current)
V = 1.5 * 2 = 3V
runo
30 Points
6 years ago
will someone post  the proper answer.plzz
Aarti Gupta
askIITians Faculty 300 Points
6 years ago
Dear student i am again explaining the question you have asked.As per your question three resistors(4,6,12 ohm respectively)are connected in parallel and then connected in series with 2ohm resistor(Rs).Now,
a).The first part of question is asking about the current in the main circuit.So first we have to find the total resistance which we suppose to designated as Rt.For parallel combination
1/Rp = 1/R1 + 1/R2 + 1/R3
1/Rp = 1/4 + 1/6 + 1/12
Rp = 12/6 = 2ohm
For total resistance,Rt = Rp + Rs (Since all three connected in series with the 2ohm resistor)
Rt = 2 + 2 = 4ohm
According to Ohm’s law,
V = I*R
I = V/R = 6/4 = 1.5A (Since the whole combination is connected to a battery of 6V)
b).Second part is asking the current through each resistor connected in parallel.Since in parallel combination current will get divided into three part each through the three resistors(I1,I2 and I3).Voltage in such combination remains same.
So I1 = V/R1 , I2 = V/R2 and I3 = V/R3 which we calculated as explained above.
3).Third part is asking the voltage across 2ohm resistor.Let it be Vs
Vs = I * Rs
For that main current which is calculated as above will be used as this resistor is connected in series so the main current will passes through it also.
Vs = 1.5 * 2 = 3V

noogler
489 Points
5 years ago
lets find parallel resistance first
 = 24/12 = 2ohmp = 1/4 + 1/6 + 1/12=12/24Rp1/R + 1/R2 + 1/R1= 1/R1/R
 total resistance=Rp + Rs = 2 + 2 = 4ohm
current in circuit=i=V/R=6/4=1.5amp
current flow is diff in all parallel resistors and potential diff is same in all parallel resistors but not same as series resistor.
Vp potential diff across parallel resistors,Vs potential diff aross series resistor
V=Vp+Vs
Vs=I(2)=(1.5)2=3V
Vp=V-Vs=6-3=3V
current through Ris            I1=Vp/R1=3/4 amp
current through  Ris           I2=Vp/R2=3/6=1/2amp
current through Ris         I3=Vp/R3=3/12=1/4amp
 
approve if it is r8
Kushagra Madhukar
askIITians Faculty 629 Points
11 months ago
Dear student,
Please find the attached solution to your problem.
 
The resultant resistance from the parallel arrangement
1/Rp = 1/4+ 1/6 + 1/12 = 6/12
Hence, Rp = 2Ω
Now total resistance in circuit = Rp + Rs = 2 + 2 = 4Ω
 
a). current in circuit, I = V/R = 6/4 = 1.5 A
 
b). Now the potential difference across the circuit will be the sum of potential drop across the two arrangements.
Hence, V = Vp + Vs
Vs = I(2) = (1.5)2 = 3V
Vp = V – Vs = 6 – 3 = 3V
current through R1, I1 = Vp/R1 =  0.75 A
current through  R2, I2 = Vp/R2 = 3/6 = 0.5 A
current through R3, I3 = Vp/R3 = 3/12 = 0.25 A
 
c). We have already calculated, Vs = 3 V
 
Thanks and regards,
Kushagra

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