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Question
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.
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Solution
Given:-
Emf of the battery, E = 100 volt
Resistance in series with battery, R' = 10 kΩ = 10000 Ω
External resistance, R = (1-100) Ω
When no external resistor is present (R = 0), current through the circuit,
\[i = \frac{E}{R'} = \frac{100}{1000} = 0 . 01 \text{ Amp.}\]
When R = 1 Ω,
\[i = \frac{100}{10000 + 1} = \frac{100}{10001}\]
\[ = 0 . 009999 A\]
When R = 100 Ω,
\[i = \frac{100}{10000 + 100}\]
\[ = \frac{100}{10100} = 0 . 009900 A\]
We can see that up to R = 100 Ω, the current does not change up to two significant digits.
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