The value of the resistor, `R_(S)`, needed in the dc voltage regulator circuit shown here, equals :-

Options

A. `((V_(i)-V_(L)))/((n+1)I_(L))`
B. `((V_(i)+V_(L)))/((n+1)I_(L))`
C. `((V_(i)-V_(L)))/(nI_(L))`
D. `((V_(i)-V_(L)))/(nI_(L))`

Answer

A

Explanation

Current through resistor, `R_(s)=I_(L)+nI_(L)=(1+n)I_(L)`
In the voltage regulator circuit, the voltage across resistor `R_(s)` will be equal to the potential difference between input source and output load.
i.e. `I_(s)R_(s)=V_(i)-V_(L) rArr (1+n)I_(L)R_(s)=V_(i)-V_(L)`
So, value of the resistor, `R_(s)=(V_(i)-V_(L))/((n+1)I_(L))`