Question

two identical heating coils are first connected in series and then parallel across the potential difference. what will be the ratio of heat generated in series to that of parallel ​

Answer 1

Solution:

Let the resistance of both the coils be R.

$\blacksquare$Coils connected in series:

The equivalent resistance of the combination is,

⇒ Rs = R₁ + R₂

⇒ Rs = R + R

⇒ Rs = 2R

The heat generated in the coil is given by,

⇒ H = I²Rt

⇒ H = I²(Rs)t

⇒ H = I² x 2R x t

⇒ H = 2RI²t ....(1)

$\blacksquare$Coils are connected in parallel:

The equivalent resistance of the combination is,

⇒ 1 /Rp = 1 /R₁ + 1 /R₂

⇒ 1 /Rp = 1 /R + 1 /R

⇒ Rp = R/2

The heat generated in the coil is given by,

⇒ H '= I²Rt

⇒ H '= I²(Rp)t

⇒ H '= I² x R /2 x t

⇒ H '= RI²t /2 ....(2)

The ratio of heat generated:

⇒ H / H' = 2RI²t x 2  / RI²t

⇒ H / H' = 4 / 1

⇒ H: H' = 4:1

The ratio of heat generated in series to that of parallel ​is 4:1.