**We use two expressions: (i) H2R ; (ii) V2t/R for calculating the enrgy consumed by a device. Out of these two expressions the first expression indicates that the energy consumed is directly prportional to R whwreas the second expression indicates that the energy consumed is inversely prportional to R. How can we explain the seemigly different dependence of H on R in these expressions?**

**We use two expressions: (i) H2R ; (ii) V2t/R for calculating the enrgy consumed by a device. Out of these two expressions the first expression indicates that the energy consumed is directly prportional to R whwreas the second expression indicates that the energy consumed is inversely prportional to R. How can we explain the seemigly different dependence of H on R in these expressions?**

### Asked by Abha | 21st Sep, 2015, 11:11: PM

###
The first equation H R

We write, Work Done, W = Q × V = I × t × I × R = I² × R × t

All the electrical work done or all the electrical energy consumed is converted into the heat energy.

Therefore, replacing work done to heat produced.

Hence, H = I² × R × t

The second equation, E V²t/R

Electrical energy = power × t = V²t/R (since, P = V²t/R)

Hence, electrical energy consumed by an electrical appliance is given by the product of its power rating and time for which it is used.

This is how these expressions show seemingly different dependence on R.

The first equation H R

We write, Work Done, W = Q × V = I × t × I × R = I² × R × t

All the electrical work done or all the electrical energy consumed is converted into the heat energy.

Therefore, replacing work done to heat produced.

Hence, H = I² × R × t

The second equation, E V²t/R

Electrical energy = power × t = V²t/R (since, P = V²t/R)

Hence, electrical energy consumed by an electrical appliance is given by the product of its power rating and time for which it is used.

This is how these expressions show seemingly different dependence on R.

### Answered by Priyanka Kumbhar | 22nd Sep, 2015, 11:31: AM

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