Question

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

• A. 8.33 amp
• B. 10 amp
• C. 12.5 amp
• D. 18.5 amp

Answer 1

The correct option is B 10 amp

At current $I=0$, resistance$=R_o=20\Omega$

Increase in resistance$=\Delta R=\frac{I}{2}$

$R=R_o+\Delta R$

$⟹R=20+\frac{I}{2}$

Now, $E=IR$

$⟹250=I(20+\frac{I}{2})$

$⟹I^2+40I-500=0$

$⟹(I+50)(I-10)=0$

Hence, $I=10A$

Answer-(B)