NCERT Class 10 Science Chapter 11 Activities — Electricity

NCERT Class 10 Science — Electricity, Activities 11.1 to 11.6 on pages 175 to 185.

Also here. Solutions to the end-of-chapter questions for this chapter and the in-text questions are on their own pages.

Six activities, and unusually for this book they form a single unbroken argument, each one built on the apparatus of the last.

• Activity 11.1 finds that V/I is constant for a wire — Ohm’s law.
• Activity 11.2 finds that the constant is different for different components, which is what resistance means.
• Activity 11.3 asks what the resistance of a wire depends on.
• Activities 11.4 and 11.5 take a series combination and find, in turn, that the current is the same everywhere and that the voltages add.
• Activity 11.6 does the same for a parallel combination and finds the currents add instead.

The last three are the ones examination questions come from, and they are worth doing as a block because 11.5 literally begins “In Activity 11.4, insert a voltmeter…”.

Key insight. Series and parallel differ in what is shared. In series there is one path, so the current is common and the voltages divide. In parallel the branches join the same two points, so the voltage is common and the currents divide. Every formula in this chapter — and every circuit question in the Exercises — comes out of deciding which of those two applies before touching any arithmetic.

Activity 11.1

Set up the circuit of Fig. 11.2: a nichrome wire XY about 0.5 m long, an ammeter, a voltmeter and four cells of 1.5 V each. Use one cell first and note the ammeter reading I and the voltmeter reading V. Repeat with two cells, then three, then four. Calculate V/I for each pair.

What you should observe. Both readings rise together, and their ratio does not change.

Why four cells rather than a rheostat. Adding cells one at a time gives four clean, well-separated points rather than a continuously varying reading, and each point is stable long enough to write down. Four points are enough to see a straight line and not enough to be tedious.

Why nichrome specifically. Its resistance changes relatively little as it warms, so V/I stays constant over the range used. A copper wire of similar length would have so little resistance that the readings would be dominated by the ammeter and the connecting leads.

What goes wrong. Leaving the current on between readings. The wire heats, its resistance drifts upward, and the last points sag away from the straight line — which looks like a failure of Ohm’s law and is not. Close the key, read both meters, open the key.

Activity 11.2

Take a nichrome wire, a torch bulb, a 10 W bulb, an ammeter (0–5 A) and a plug key. Connect four 1.5 V cells in series with the ammeter, leaving a gap XY as in Fig. 11.4. Put each component in turn into the gap and note the current.

What you should observe. The same battery drives quite different currents through different things.

Why this is the definition of resistance, not just an illustration of it. Activity 11.1 established that V/I is constant for one wire. This shows the constant is a property of the component — different components, different constants. That is exactly what resistance is, and the chapter’s explanation is in terms of electrons “restrained by the attraction of the atoms among which they move”.

What goes wrong. Using an ammeter on too coarse a range. A 0–5 A meter reads a torch bulb’s current as a barely-moved needle, and the comparison the activity depends on is lost in the reading error. If a lower range is available, use it for the bulbs.

Activity 11.3

Complete a circuit of a cell, an ammeter, a nichrome wire of length l and a plug key, as in Fig. 11.5. Note the current. Then replace the wire with one of length 2l of the same thickness, then with a thicker nichrome wire of length l, then with a wire of a different material — say copper — of the same length and thickness.

What you should observe. Three separate dependences, isolated one at a time.

Why the design matters more than the readings. This is a controlled experiment, and each step changes exactly one variable. Comparing a long thin copper wire with a short thick nichrome one would tell you nothing, because three things differ at once. The chapter’s sequence is careful about this, and it is worth making the class say which variable is being changed before each swap.

What goes wrong. Loose crocodile clips. The contact resistance at a bad joint can be larger than the wire being measured, so the “result” is really a measurement of the clip. Clean the wire ends and clamp them firmly — and if a reading looks odd, wiggle the connections before believing it.

Activity 11.4

Join three resistors of different values in series — 1 Ω, 2 Ω and 3 Ω will do — with a battery of 6 V, an ammeter and a plug key, as in Fig. 11.6. Note the ammeter reading. Then move the ammeter to a different point between the resistors and read it again. And again.

What you should observe. The reading does not change, wherever the ammeter is put.

Why this is not obvious, and worth testing. Students routinely expect the current to be “used up” as it passes through each resistor, so that less arrives at the third than at the first. Moving the ammeter and getting the same number three times is the cleanest possible refutation. Charge is not consumed by a resistor; it is only impeded.

How the chapter turns it into a formula. If the current is common and the voltages add (Activity 11.5), then $V = V_1 + V_2 + V_3$ becomes $IR_s = IR_1 + IR_2 + IR_3$, so

$$R_s = R_1 + R_2 + R_3$$

The chapter’s worked example, recomputed. A 20 Ω lamp and a 4 Ω conductor in series on a 6 V battery: total 24 Ω, so I = 6/24 = 0.25 A, and the voltages are 20 × 0.25 = 5 V and 4 × 0.25 = 1 V, which sum back to 6 V.

What goes wrong. Breaking the circuit to move the ammeter and reconnecting it the wrong way round, so the needle kicks backwards. It is worth noting which terminal was which before unclipping anything.

Activity 11.5

In the circuit of Activity 11.4, connect a voltmeter across the ends X and Y of the whole series combination and note the reading, V. Compare it with the potential difference across the battery terminals. Then take the key out, move the voltmeter across the first resistor alone and read V₁; then across the second and third for V₂ and V₃. Find the relation between V, V₁, V₂ and V₃.

What you should observe. The three separate readings add up to the whole.

Why it is the other half of Activity 11.4. Together they give the two facts a series circuit runs on: current common, voltages additive. Neither alone is enough to derive $R_s = R_1 + R_2 + R_3$.

Why the voltmeter goes across and the ammeter goes in. A voltmeter measures a difference between two points, so it is connected in parallel with the component. An ammeter measures what flows through, so it must be in the path. Getting this the wrong way round is the single most common wiring error in the chapter — and an ammeter connected across a battery is a short circuit.

What goes wrong. Reading the battery’s terminal voltage as exactly its rated value. Four 1.5 V cells will not deliver 6.00 V under load, because the cells have internal resistance. The comparison the activity asks for — V against the battery voltage — is meant to be close, not identical, and old cells make it noticeably less so.

Activity 11.6

Make a parallel combination XY of three resistors R₁, R₂, R₃ with a battery, a plug key and an ammeter, as in Fig. 11.10, and a voltmeter across the combination. Note the ammeter reading I and the voltmeter reading V. Then take the plug out, remove both meters, and insert the ammeter in series with R₁ alone to read I₁. Do the same for R₂ and R₃. Find the relation between I, I₁, I₂ and I₃.

What you should observe. The branch currents add up to the total.

Why the equivalent resistance is smaller than any single resistor. This is the result students find hardest to accept, and the activity makes it concrete: adding another branch adds another path, so more current flows in total for the same voltage — and more current for the same voltage means less resistance. The reciprocal formula follows from applying Ohm’s law to each branch at the common voltage.

The chapter’s worked example, recomputed. 5 Ω, 10 Ω and 30 Ω in parallel across 12 V: the branch currents are 12/5 = 2.4 A, 12/10 = 1.2 A and 12/30 = 0.4 A, totalling 4 A. The equivalent resistance is $1/R_p = 1/5 + 1/10 + 1/30 = 1/3$, so $R_p = $ 3 Ω — smaller than the smallest branch, and 12/3 = 4 A agrees with the sum.

Why household wiring is parallel. Each appliance gets the full mains voltage regardless of the others, and switching one off does not break the path for the rest. In series, everything would share the voltage and one failure would stop the lot.

What goes wrong. Leaving the voltmeter connected while measuring branch currents, which is what the instruction to “remove the ammeter and voltmeter” is guarding against. Also worth watching: a parallel combination draws more total current than any single resistor, so the battery runs down noticeably faster and readings drift if the key is left in.

Common mistakes

• Blaming Ohm’s law when the last points of Activity 11.1 sag. That is the wire warming up and its resistance rising. Take readings quickly and open the key between them.
• Thinking current is used up along a series circuit. Activity 11.4 exists to disprove exactly this. The ammeter reads the same wherever it is placed.
• Connecting the ammeter in parallel or the voltmeter in series. Ammeter in the path, voltmeter across the component. An ammeter across a battery is a short circuit.
• Expecting a parallel combination to have more resistance than its parts. It always has less than the smallest one — more paths mean more current for the same voltage.
• Changing two things at once in Activity 11.3. Length, thickness and material must be varied one at a time, or the result cannot be attributed to any of them.
• Trusting a reading through a loose clip. Contact resistance at a bad joint can exceed the component being measured, and it is the commonest cause of a result that makes no sense.

Practise next

• The end-of-chapter Exercises for this chapter, where Questions 4, 14 and 15 use the series and parallel results of Activities 11.4 to 11.6 on harder combinations, and Question 18 asks why domestic circuits are wired in parallel.
• The in-text questions of this chapter, twenty-three across seven boxes, which rehearse Ohm’s law and resistor combinations in shorter form before the Exercises.
• The activities of Chapter 12, where the current whose behaviour is established here becomes the source of a magnetic field.
• Chapter 12, Magnetic Effects of Electric Current, which takes the same circuits and asks what they do to a compass needle.