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).

Given-
R₁ = 4ohm
R₂ = 6ohm
R₃ = 12ohm
R_s = 2ohm (Series resistor)
Potential difference,V = 6V
Let the resistance of all three resistors which are connected in parallel be R_p
Then,
1/R_p = 1/R₁ +1/R₂ + 1/R₃
1/R_p = 1/4 + 1/6 + 1/12
1/R_p = 6/12
or,R_p = 12/6 = 2ohm
Let total resistance be R_t = R_p +R_s
R_{t =} 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

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(R_s).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 R_t.For parallel combination
1/R_p = 1/R₁ + 1/R₂ + 1/R₃
1/R_p = 1/4 + 1/6 + 1/12
R_p = 12/6 = 2ohm
For total resistance,Rt = R_p + R_s (Since all three connected in series with the 2ohm resistor)
R_t = 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 V_s
V_s = I * R_s
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.
V_s = 1.5 * 2 = 3V