Q133 / 180 · KCET 2024 · Physics

The electric current flowing through a given conductor varies with time as shown in the graph below. The number of free electrons which flow through a given cross-section of the conductor in the time interval $0 \leq t \leq 20 \mathrm{~s}$ is Figure

  • Correct answer
    A
    $3.125 \times 10^{19}$
  • B
    $1.6 \times 10^{19}$
  • C
    $6.25 \times 10^{18}$
  • D
    $1.625 \times 10^{18}$

Solution

Total charge flowing the cross-section of the conductor is equal to area under I-t graph. $\therefore Q=\frac{(100+300)}{2} 10 \times 10^{-3}+(20-10) \times 300 \times 10^{-3}$ $=1+3=4 C$ Since, $Q=n e$ $\therefore \quad n=\frac{Q}{e}=\frac{4}{1.6 \times 10^{-19}}=3.125 \times 10^{19}$

Hence, the correct answer is option: 'A'.

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