Question

In the circuit above the resistance R has a value that depends on the current. R is 20 ohms when I is zero and the amount of increase in resistance is numerically equal to one half of the current. What is the value of current I in circuit?

Answer 1

According to question, $R=20+\frac{i}{2}$

Now using KVL in given loop, $iR=250$

$i(20+i/2)=250$

$20i+\frac{i^2}{2}=250$

$i^2+40i-500=0$

$i^2+50i-10i-500=0$

$i=10A$

R to be negative not possible.