The current flowing through a conductor connected across a source is 2 A and 1.2 A at $0^{\circ} \mathrm{C}$ and $100^{\circ} \mathrm{C}$ respectively. The current flowing through the conductor at $50^{\circ} \mathrm{C}$ will be \_\_\_\_ $\times 10^{2} \mathrm{~mA}$.

JEE Main · 2023 · 12 Apr 2023 · Shift 1 · Current Electricity

The current flowing through a conductor connected across a source is 2 A and 1.2 A at

0^{\circ} C

and

10 0^{\circ} C

respectively. The current flowing through the conductor at

5 0^{\circ} C

will be ____

\times 1 0^{2} mA

Answer: 15

The source voltage is fixed, so

V = i R

gives

i \propto \frac{1}{R}

, and the resistance varies as

R_{t} = R_{0} (1 + α t)

. At

0^{\circ} C

V = 2 R_{0}

; at

10 0^{\circ} C

V = 1.2 R_{0} (1 + 100 α)

. Equating these,

1 + 100 α = \frac{2}{1.2} = \frac{5}{3}

, so

100 α = \frac{2}{3}

and

50 α = \frac{1}{3}

. At

5 0^{\circ} C

i_{50} = \frac{V}{R _{0} ( 1 + 50 α )} = \frac{2}{1 + \frac{1}{3}} = \frac{2}{4/3} = 1.5 A

. Since

1.5 A = 1500 mA = 15 \times 1 0^{2} mA

, the value is

15

JEE Main · 2023 · 12 Apr 2023 · Shift 1 · Integer answer