Question

The cold resistance of a certain gas filled with tungsten lamp is 18.2Ohms and its hot resistance operating voltage of 110 V is 202Ohms, find the current
1) at the instant of switching on
2) The normal working current.

Answer 1

Hint: In this question we have been asked to calculate the current in the tungsten filament at the instant when it is switched and when it is working normally. We have been given the operating voltage as 110 V. Its starting resistance or cold resistance is given as 18.2 Ohms and hot or normal resistance is given as 202 Ohms. Therefore, we shall use Ohm's law to calculate the current.
Formula Used: \[I=\dfrac{V}{R}\]

Complete answer:
In this question we have been asked to calculate the current of the lamp at the instant when it is switched on.
From Ohm's law, we know,
\[I=\dfrac{V}{R}\]
a) Let \[{{I}_{1}}\] be the current when the lamp is switched on, the filament is now cold. Therefore, the resistance is 18.2 Ohms.
Therefore, we get
\[{{I}_{1}}=\dfrac{110}{18.2}\]
On solving,
\[{{I}_{1}}=6.04A\]
b) Now, the resistance of the lamp shall be taken as the hot resistance as the filament gets heated up after some time the lamp is on.
Therefore,
\[{{I}_{2}}=\dfrac{110}{202}\]
On solving,
\[{{I}_{2}}=0.54A\]
Therefore, the starting current is 6.04 A and the normal working current is 0.54 A.

Note:
From the above question we can say that the filament uses a larger amount of current to start than the normal working current. This happens because the filament takes time to heat up. Once the filament is heated the resistance increases and from Ohm's law, we know that current is inversely proportional to resistance. Therefore, the normal working current is usually less.