Chapter 18, Problem 10Q

To determine

To explain:

The bulb, that will draw more current and the one which will have a higher resistance.

Answer to Problem 10Q

Solution:

The 100W bulb draws more current but the 75W bulb has more resistance.

Explanation of Solution

Formula used: The Ohm’s law tells that the ratio of voltage drop ( V ) and the current ( I ) passing through a resistance ( R ) is ideally constant which is equal to the value of that resistance itself, i.e.,

  $R=\frac{V}{I}$

The power consumption by a resistor is given as,

  $P=I^{2}R=V\times I=\frac{V^2}{R}$

We are assuming that both the bulbs are being used in the same country, i.e., the voltage supply to both the bulbs isthe same.

Now to determine which bulb draws more current, we can use the formula $P=V\times I$ which tells, if V is constant, then that bulb will draw more current in which more power is dissipated. Therefore, the 100-W bulb will draw more current.

Similarly, to determine which bulb offers more resistance, we can use the formula $P=\frac{V^2}{R}$ which tells, if V is constant, then that bulb will offer more resistance in which less power is dissipated. Therefore, the 75-W bulb will offer more resistance.

Conclusion:

The higher the power consumption,the more will be the current drawn, and the lower the power consumption, the higher will be the resistance of the filament of the bulb.