Chapter 11 · Electricity

NCERT Class 10 Science Chapter 11 Intext Questions (Page 181)

All 5 questions of NCERT Class 10 Science Chapter 11 Intext Questions (Page 181) — Electricity — in the book's order, each with its answer and a step-by-step solution.

1. Q1
   On ​what ​factors ​does ​the resistance of a conductor ​depend?
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   It depends on length, area of cross-section, nature of the material (resistivity) and temperature: $R=\rho \frac{l}{A}$.

   The resistance of a conductor depends on: (i) its length $l$ — resistance is directly proportional to length, $R\propto l$; (ii) its area of cross-section $A$ — resistance is inversely proportional to it, $R\propto 1/A$, so a thicker conductor has less resistance; (iii) the nature of its material, entering through the resistivity $\rho$; and (iv) its temperature — both $R$ and $\rho$ change when the conductor is heated, which is why Ohm's law is stated for a fixed temperature. The first three are collected in $R=\rho l/A$.

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2. Q2
   Will current flow more easily through ​a ​thick wire ​or a thin wire of the same material, when ​connected to ​the same source? Why?
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   The thick wire, because its larger cross-section gives lower resistance, so more current flows at the same potential difference.

   Current flows more easily through the thick wire. Both wires are of the same material and the same length, so $\rho$ and $l$ are fixed and $R=\rho l/A$ leaves the resistance depending only on the area of cross-section, inversely: $R\propto 1/A$. The thick wire has the larger area, so it has the smaller resistance. The same source puts the same potential difference $V$ across each, so by Ohm's law $I=V/R$ the wire with the smaller resistance carries the larger current. Hence the thick wire draws more current — it offers an easier path.

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3. Q3
   Let ​the ​resistance of ​an electrical component ​remains constant while the potential difference across the two ​ends of the ​component decreases to half of its former value. What change ​will occur in the current through it?
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   The current is also halved, since $I=V/R$ and $R$ is constant.

   The current is also halved. With the resistance constant, Ohm's law $I=V/R$ makes the current directly proportional to the potential difference, so replacing $V$ by $V/2$ gives $I^{\prime }=(V/2)/R=I/2$: the new current is half the former current.

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4. Q4
   Why ​are ​coils of electric toasters ​and electric irons ​made ​of an alloy rather than a ​pure metal?
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   An alloy has much higher resistivity, so it heats more for the same current, and it does not oxidise readily when red hot.

   Because an alloy suits a heating element in two ways that a pure metal does not. First, the resistivity of an alloy is generally much higher than that of its constituent metals — nichrome is about $100\times 10^{-6}\Omega \text{m}$ against about $10\times 10^{-8}\Omega \text{m}$ for iron or nickel — so a coil of ordinary length and thickness has a large resistance and, by $H=I^{2}Rt$, gives out a great deal of heat for the current drawn. Second, alloys do not oxidise (burn) readily at high temperatures, so the coil can be kept red hot in air for hours without corroding away. A pure-metal coil of the same size would hardly heat up and would soon oxidise and break.

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5. Q5
   Use the ​data in Table ​11.2 to answer the following –

   1. (a)​Which among ​iron ​and mercury is a better conductor?
   2. (b)Which ​material is the best ​conductor?
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   (a) Iron, as its resistivity is lower than mercury's; (b) silver, which has the lowest resistivity in the table.

   (a) Iron is the better conductor. Table 11.2 gives ${\rho }_{\text{Fe}}=10.0\times 10^{-8}\Omega \text{m}$ against ${\rho }_{\text{Hg}}=94.0\times 10^{-8}\Omega \text{m}$; since $R=\rho l/A$, the smaller resistivity means the smaller resistance for identical wires, and iron's is smaller by a factor of about $9.4$. (b) Silver is the best conductor, with the lowest resistivity in the table, ${\rho }_{\text{Ag}}=1.60\times 10^{-8}\Omega \text{m}$ — just below copper's $1.62\times 10^{-8}\Omega \text{m}$.

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