A heater coil is cut into two parts of equal length and one of them is used in the heater. The ratio of the heat produced by this half coil to that by the original coil is

Question

A heater coil is cut into two parts of equal length and one of them is used in the heater. The ratio of the heat produced by this half coil to that by the original coil is (A) 2: 1 (B) 1: 2 (C) 1: 4 (D) 4: 1

Tardigrade Admin · Accepted Answer

P=(V2/R) ⇒ P propto (1/R) and R propto l ∴ P propto (1/l) ⇒ (P1/P2)=(l2/l1)=(2/1)

Q. A heater coil is cut into two parts of equal length and one of them is used in the heater. The ratio of the heat produced by this half coil to that by the original coil is

2 : 1

1 : 2

1 : 4

4 : 1

$P = \frac{V ^{2}}{R} \Rightarrow P \propto \frac{1}{R}$ and $R \propto l$
$∴ P \propto \frac{1}{l} \Rightarrow \frac{P _{1}}{P _{2}} = \frac{l _{2}}{l _{1}} = \frac{2}{1}$

Q. A heater coil is cut into two parts of equal length and one of them is used in the heater. The ratio of the heat produced by this half coil to that by the original coil is

2 : 1

1 : 2

1 : 4

4 : 1

P=RV2​⇒P∝R1​ and R∝l ∴P∝l1​⇒P2​P1​​=l1​l2​​=12​

$P = \frac{V ^{2}}{R} \Rightarrow P \propto \frac{1}{R}$ and $R \propto l$
$∴ P \propto \frac{1}{l} \Rightarrow \frac{P _{1}}{P _{2}} = \frac{l _{2}}{l _{1}} = \frac{2}{1}$