Question

Question 12. Two conducting of same 1
material and equal length and
diameter are first connected in series
and then in parallel in a circuit across
the same potential difference, the
ratio of heat produced in series and
parallel combination would be
O 1/2
O 2/1
O 1/4
04/1​

Answer 1

Two conducting of same material and equal length and diameter are first connected in series and then in parallel in a circuit.

For series:

Rs = R1 + R2

(as they're made of same material. So, R1 = R2 = R)

Rs = R + R

Rs = 2R

For parallel:

1/Rp = 1/R + 1/R

1/Rp = 2/R

Rp = R/2

We have to find the the ratio of heat produced in series and parallel combination.

For series:

H(s) = V²/Rs × t

H(s) = V²/(2R) × t ...............(1st equation)

For parallel:

H(p) = V²/Rp × t

H(p) = V²/(R/2) × t

H(p) = 2V²/R × t ...................(2nd equation)

Divide (1st equation) and (2nd equation)

H(s)/H(p) = [V²/(2R) × t]/[2V²/R × t]

H(s)/H(p) = 1/2 × 1/2

H(s)/H(p) = 1/4

Therefore, the ratio of heat produced in series and parallel combination is 1:4.

Option c) 1/4

Answer 2

Answer: Since the two wires have same material, length and diameter, they have the same resistance. Let the resistance of each wire be R.

Let applied potential difference be V.

R series​=R1​+R2​

            =R+R=2R

P series​=V2/R series​

            =V2/(2R)..........(i)

R parallel​1​=R1​1​+R2​1​

R parallel​=R/2

P parallel​=V2/R   parallel​

             =2V2/R............(ii)

Dividing (ii) from (i),

P parallel / ​P series​​=1/4

Explanation: