Question

Heater of an electric kettle is made of a wire of length $L$ and diameter d. It takes $4$ minutes to raise the temperature of $0.5\, kg$ water by $40\, K$. This heater is replaced by a new heater having two wires of the same material, each of length $L$ and diameter $2 \,d$. The way these wires are connected is given in the options. How much time in minutes will it take to raise the temperature of the same amount of water by $40\, K$ ?

• A. 4 if wires are in parallel
• B. 2 if wires are in series
• C. 1 if wires are in series
• D. 0.5 if wires are in parallel.

Answer 1

Answer: (B), (D)

$H =\frac{ V ^{2}}{ R } 4=\frac{ V ^{2}}{ R / 2}$
$ t _{1}=\frac{ V ^{2}}{ R / 8} t _{2}$
$t _{1}=2 \min$
$t _{2}=0.5 \min$