Ohm's Law

In the circuit, $n = 1.875 \times 10^{21}$ electrons are flowing in $t = 50$ seconds

Hence, current passing through the circuit ,

$I = \frac{ne}{t}$

$= \frac{1.875 \times 10^{21} \times1.6 \times 10^{-19}}{50} = 6 A$

Total energy dissipated from the resistor,

$E = I^{2}Rt = n \times w$ where $w$ = energy given by cell to each electron = $4.8 \times 10^{-18} J$

$\therefore R = \frac{nw}{I^{2}t}$

$\therefore R = \frac{1.875 \times 10^{21} \times 4.8 \times 10^{-18}}{(6)^{2}50}$

$\therefore R = 5$

The charge q is an integral multiple of e i.e ${Q}={I}{t}={q}{n}$ Substituting the given values we get ${Q}={I}\times{(50)}=({1.6^-19})\times({1.875^-19})$ ${Q}={I}\times{(50)}={300}$ from which we get ${Q}={300C}$ and ${I}={6A}$ The total energy of the electrons is given by ${W}=({1.875^+ 21})\times({4.8^-19})$ ${W}={9000J}$ But ${W}={Q}{V}$ Thus ${V}=\frac{W}{Q}$ ${V}=\frac{9000}{300}$ ${V}={30V}$ From ${v}={I}{R}$ ${R}=\frac{V}{I}$ ${R}=\frac{30}{6}$ Therefore the resistance of the resistor ${R}=\boxed{5ohms}$

Total energy supplied by the battery is 1.875×10^21×4.8×10^-18=9000J

The consumed power is 9000/50=180Watt The net current through the circuit is 1.875×10^21×1.602×10^-19/50=6A So the resistance is180/36=5ohm

Every 50 seconds 1.875 X 10^21 electrons pass a point P,

Therefore, Number of electrons pass the point in 1 sec can be found out to determine the current

No. of electrons pass in one sec = (1.875 x10^21) / 50

                                                          = 37.5 x 10^18 electrons/sec.
             From Definiton,

                               1A = 6.24 x10^18 electrons/ sec

              Therefore  I = (37.5 x 10^18 electrons)/(6.24 x10^18 electrons)
                                     = 6A.

Each Electron carries 4.8 x 10^-18 Joules of energy,

Therefore Voltage = electric potential energy/ columb.

1C = 6.24 x 10^18 electrons

V = 6.24 x 10^18 x 4.8x 10^-18

V = 30 V.

Now Just apply Ohm's Law

R =V/I = 30/6 = 5 Ohm

From Ohm's law we know that R= $\frac{V}{I}$ . E=vit . v= $\frac{E}{it}$ .total energy is given by $4.8 \times 10^{-18} times 1.875 \times 10^{21}$ =9000. R= $\frac{9000}{6 \times 50 \times \times 6}$ =5 .