Question

A tap supplies water at 22${}^0$ C . A man takes 1 litre per minute at 37${}^0$ from the geyser . If the mains supply is 210V, then the current flowing in the geyser is :

• A. 7.5A
• B. 2.5A
• C. 5.0A
• D. 10A

Answer 1

The correct option is C 5.0A

Given $m=1$ liter
$t=1$ min
$\Delta \theta ={37}^{\circ }-{22}^{\circ }={15}^{\circ }$ C
The heat required by the water per second to change its temperature from ${22}^{\circ }$ C to ${37}^{\circ }$ C is
$\frac{dQ}{dt}=\frac{dm}{dt}C\left(\Delta \theta \right))$
$\frac{dQ}{dt}=\frac{1000}{60}\left(1\right)\left(15\right))$
$\frac{dQ}{dt}=250$ cal s${}^{-1}$
$\frac{dQ}{dt}=250\times 4.2$ J s${}^{-1}$
$\frac{dQ}{dt}=1050$ J s${}^{-1}$
Now, the current through the gyser is
$I=\frac{\frac{dQ}{dt}}{V}$

Hence $I=\frac{1050}{418}=5A$