Q. 22

A battery of emf 100 V and a resistor of resistance 10 kΩ are joined in series. This system is used as a source to supply current to an external resistance R. If R is not greater than 100 Ω, the current through it is constant up to two significant digits. Find its value. This is the basic principle of a constant-current source.

Answer :

10mA

Given,


Emf of the battery, E= 100V


Resistance of series resistor, r= 10kΩ=10000kΩ


Resistance of external resistor, R=0-100Ω


Formula used:


A constant-current source is a power source that supply constant current to an external load, even if there is a change in load resistance.


When the battery is connected to the external resistance that vary from 0 to 100 Ω, the effective resistance will change across the potential difference provided by the battery.



Solution:


Let’s find out the current when R=0Ω or when there is no external resistance is connected,


We know that, current i for a series resistor connection is



By substituting the known values, we get i as,



Now let’s take R as 2 Ω (or a low value like 1 Ω or so)


The value of current, i is



Where Rtot is the effective resistance across the battery. From the figure, Rtot can be calculated as,



Hence by putting R=2 Ω, we get i as,



Similarly, by putting R=100Ω , the highest possible, we get the current i as,



So, as the principle predicted, the value of the current, 1mA, does not change much, or it stays consistent till two significant digits.


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