Current Electricity Charging Discharging Of Capacitors Question 91
Question: Water boils in an electric kettle in 15 minutes after switching on. If the length of the heating wire is decreased to $ 2/3 $ of its initial value, then the same amount of water will boil with the same supply voltage in
[MP PMT 1994]
Options:
A) 15 minutes
B) 12 minutes
C) 10 minutes
D) 8 minutes
Show Answer
Answer:
Correct Answer: C
Solution:
$ H=\frac{V^{2}}{R}t $ Since supply voltage is same and equal amount of heat will produce,
Therefore $ \frac{R _{1}}{t _{1}}=\frac{R _{2}}{t _{2}} $ or $ \frac{R _{1}}{R _{2}}=\frac{t _{1}}{t _{2}} $ …..(i) But $ R\propto l $
Therefore $ \frac{R _{1}}{R _{2}}=\frac{l _{1}}{l _{2}} $ …..(ii) By (i) and (ii), $ \frac{l _{1}}{l _{2}}=\frac{t _{1}}{t _{2}} $ …..(iii) Now $ l _{2}=\frac{2}{3}l _{1} $
Therefore $ \frac{l _{1}}{l _{2}}=\frac{3}{2} $ \ By equation (iii), $ \frac{3}{2}=\frac{15}{t _{2}} $
Therefore $ t _{2}=10 $ minutes
BETA
