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An electrical coil is connected in series with resistance of X ohm across the 240 volt mains .the coil being immersed in 1kg at 20degreeC .The temperature of water rises to boiling point in 10 minutes..when a second heating experiments is made with the resistance X short circuited.the time required to develop the same quantity of heat is reduced to 6 minutes.calculate the value of X.

$S u p p o s e t h e r e s i s \tan c e o f c o i l = R T h e n c u r r e n t I = \frac{240}{X + R} N o w u \sin g t h e f o r m u l a, I^{2} R T = m S θ {(\frac{240}{X + R})}^{2} R \times 10 \times 60 = 1 \times 4200 \times (100 - 20) O R {(\frac{240}{X + R})}^{2} R = 560 - - - (a) W h e n t h e r e s i s \tan c e X i s s h o r t c i r c u i t e d, t h e n ({\frac{240}{R})}^{2} R \times 6 \times 60 = 4200 \times (100 - 20) O n s o l v i n g, w e g e t R = \frac{432}{7} o h m P u t t i n g t h i s v a l u e o f R i n (a), w e g e t {(\frac{240}{X + \frac{432}{7}})}^{2} \times \frac{432}{7} = 560 O r X = 18 o h m$

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