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(a) Six lead-acid type of secondary cells each of emf $2.0 \mathrm{~V}$ and internal resistance $0.015 \Omega$ are joined in series to provide a supply to a resistance of $8.5$ $\boldsymbol{\Omega}$. What are the current drawn from the supply and its terminal voltage?
(b) A secondary cell after long use has an emf of 1.9 $V$ and a large internal resistance $380 \Omega$. What maximum current can be drawn from the cell? Could the cell drive the starting motor of a car?
(b) A secondary cell after long use has an emf of 1.9 $V$ and a large internal resistance $380 \Omega$. What maximum current can be drawn from the cell? Could the cell drive the starting motor of a car?
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(a) Given, number of secondary cells, $\mathrm{N}=6$,
E.m.f. of each cell, $\mathrm{E}=2.0 \mathrm{~V}$
Internal resistance of each cell, $r=0.015 \Omega$,
External resistance, $\mathrm{R}=8.5 \Omega$
By formula, current,
$I=\frac{N E}{R+N r}=\frac{6 \times 2}{8.5+6 \times 0.015}$ $=\frac{12}{8.5+0.09}=1.397 \mathrm{~A}$.
Terminal voltage $\mathrm{V}=\mathrm{IR}=\frac{12 \times 8.5}{8.59}$
$=11.874 \mathrm{~V}$
(b) Given, $\mathrm{E}=1.9 \mathrm{~V}, \mathrm{r}=380 \Omega, \mathrm{I}_{\max }=$ ?
Maximum current can be drawn by short circuit, $\mathrm{I}_{\max }=\frac{\mathrm{E}}{\mathrm{r}}=\frac{1.9}{380}=0.005 \mathrm{~A}$.
Which cannot start a car, because a starter motor requires a large current $(\approx 700 \mathrm{~A}$ ) for few seconds.
E.m.f. of each cell, $\mathrm{E}=2.0 \mathrm{~V}$
Internal resistance of each cell, $r=0.015 \Omega$,
External resistance, $\mathrm{R}=8.5 \Omega$
By formula, current,
$I=\frac{N E}{R+N r}=\frac{6 \times 2}{8.5+6 \times 0.015}$ $=\frac{12}{8.5+0.09}=1.397 \mathrm{~A}$.
Terminal voltage $\mathrm{V}=\mathrm{IR}=\frac{12 \times 8.5}{8.59}$
$=11.874 \mathrm{~V}$
(b) Given, $\mathrm{E}=1.9 \mathrm{~V}, \mathrm{r}=380 \Omega, \mathrm{I}_{\max }=$ ?
Maximum current can be drawn by short circuit, $\mathrm{I}_{\max }=\frac{\mathrm{E}}{\mathrm{r}}=\frac{1.9}{380}=0.005 \mathrm{~A}$.
Which cannot start a car, because a starter motor requires a large current $(\approx 700 \mathrm{~A}$ ) for few seconds.
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