Page 200
1. What does an electric circuit mean?
Answer:
An electric circuit is a continuous and closed conducting path through which an electric current can flow.
2. Define the unit of current.
Answer:
The SI unit of current is the ampere (A). Current is said to be one ampere when one coulomb of charge flows through a conductor in one second.
I = Q/t or 1 A = 1 C s-1
3. Calculate the number of electrons constituting one coulomb of charge.
Answer:
Charge on one electron, e = 1.6 × 10-19 C
Total charge, Q = 1 C
Number of electrons, n = Q/e = 1 C/1.6 × 10-19 C = 6.25 × 1018
Page 202
1. Name a device that helps to maintain a potential difference across a conductor.
Answer:
A battery.
2. What is meant by saying that the potential difference between two points is 1 V?
Answer:
The potential difference between two points is said to be 1 volt if 1 joule of work is done in moving 1 coulomb of electric charge from one point to the other.
3. How much energy is given to each coulomb of charge passing through a 6 V battery?
Answer:
Energy given by battery = charge × potential difference
W = Q × V = 1 C × 6 V = 6 J
Page 209
1. On what factors does the resistance of a conductor depend?
Answer:
The resistance of a conductor depends on:
- Its length.
- Its area of cross-section.
- The nature of its material.
2. Will current flow more easily through a thick wire or a thin wire of the same material, when connected to the same source? Why?
Answer:
The current flows more easily through a thick wire than a thin wire of the same material. Reason: A thick wire has a larger area of cross-section, which reduces resistance and allows electrons to move more freely.
3. Let the resistance of an electrical component remain 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?
Answer:
According to Ohm’s law (V ∝ I), if resistance remains constant and potential difference is halved, the current also becomes half of its initial value.
4. Why are coils of electric toasters and electric irons made of an alloy rather than a pure metal?
Answer:
Coils are made of an alloy because:
- The resistivity of an alloy is much higher than that of a pure metal.
- An alloy does not undergo oxidation or burn easily, even when red hot at high temperature.
5. Use the data in Table 12.2 (in NCERT Book on Page No. 207) to answer the following: (i) Which among iron and mercury is a better conductor? (ii) Which material is the best conductor?
Answer:
(i) Resistivity of iron = 10.0 × 10-8 Ω m, Resistivity of mercury = 94.0 × 10-8 Ω m. Thus, iron is a better conductor because it has lower resistivity than mercury.
(ii) Silver (it has the lowest resistivity).
Page 213
1. Draw a schematic diagram of a circuit consisting of a battery of three cells of 2 V each, a 5 Ω resistor, an 8 Ω resistor, and a 12 Ω resistor, and a plug key, all connected in series.
Answer:
2. Redraw the circuit of Question 1, putting in an ammeter to measure the current through the resistors and a voltmeter to measure the potential difference across the 12 Ω resistor. What would be the readings in the ammeter and the voltmeter?
Answer:
The circuit is the same as in Question 1, with an ammeter connected in series with the resistors to measure the total current, and a voltmeter connected in parallel across the 12 Ω resistor to measure the potential difference.
Total voltage, V = 3 × 2 = 6 V
Total resistance, R = 5 Ω + 8 Ω + 12 Ω = 25 Ω
Current, I = V/R = 6 V/25 Ω = 0.24 A (ammeter reading)
Voltage across 12 Ω resistor, V12 = I × R12 = 0.24 A × 12 Ω = 2.88 V (voltmeter reading)
Page 216
1. Judge the equivalent resistance when the following are connected in parallel: (i) 1 Ω and 106 Ω, (ii) 1 Ω, 103 Ω, and 106 Ω.
Answer:
When resistances are connected in parallel, the equivalent resistance is smaller than the smallest individual resistance.
(i) Equivalent resistance < 1 Ω.
(ii) Equivalent resistance < 1 Ω.
2. An electric lamp of 100 Ω, a toaster of resistance 50 Ω, and a water filter of resistance 500 Ω are connected in parallel to a 220 V source. What is the resistance of an electric iron connected to the same source that takes as much current as all three appliances, and what is the current through it?
Answer:
Resistance of electric lamp, R1 = 100 Ω
Resistance of toaster, R2 = 50 Ω
Resistance of water filter, R3 = 500 Ω
Equivalent resistance Rp of the three appliances in parallel: 1/Rp = 1/R1 + 1/R2 + 1/R3 = 1/100 + 1/50 + 1/500 = 0.01 + 0.02 + 0.002 = 0.032
Rp = 1/0.032 = 31.25 Ω
Resistance of electric iron = Equivalent resistance = 31.25 Ω
Applied voltage, V = 220 V
Current, I = V/R = 220 V/31.25 Ω = 7.04 A
3. What are the advantages of connecting electrical devices in parallel with the battery instead of connecting them in series?
Answer:
Advantages of connecting electrical devices in parallel with the battery are:
- In parallel circuits, if an electrical appliance stops working due to some defect, then all other appliances keep working normally.
- In parallel circuits, each electrical appliance has its own switch, allowing it to be turned on or off independently without affecting other appliances.
- In parallel circuits, each electrical appliance gets the same voltage (220 V) as that of the power supply line.
- In parallel connection, the overall resistance of the household circuit is reduced, allowing higher current from the power supply.
4. How can three resistors of resistances 2 Ω, 3 Ω, and 6 Ω be connected to give a total resistance of (i) 4 Ω, (ii) 1 Ω?
Answer:
(i) To get a total resistance of 4 Ω, connect the 2 Ω resistor in series with the parallel combination of 3 Ω and 6 Ω.
Parallel resistance of 3 Ω and 6 Ω: 1/Rp = 1/3 + 1/6 = 2/6 + 1/6 = 3/6 = 1/2 ⇒ Rp = 2 Ω
Total resistance = 2 Ω + 2 Ω = 4 Ω
(ii) To obtain a total resistance of 1 Ω, connect the 2 Ω, 3 Ω, and 6 Ω resistors in parallel.
1/Rp = 1/2 + 1/3 + 1/6 = 3/6 + 2/6 + 1/6 = 6/6 = 1 ⇒ Rp = 1 Ω
5. What is (i) the highest, (ii) the lowest total resistance that can be secured by combinations of four coils of resistance 4 Ω, 8 Ω, 12 Ω, 24 Ω?
Answer:
(i) Highest resistance is obtained by connecting the four coils in series.
R = 4 Ω + 8 Ω + 12 Ω + 24 Ω = 48 Ω
(ii) Lowest resistance is obtained by connecting the four coils in parallel.
1/Rp = 1/4 + 1/8 + 1/12 + 1/24 = 6/24 + 3/24 + 2/24 + 1/24 = 12/24 = 1/2 ⇒ Rp = 2 Ω
Page 218
1. Why does the cord of an electric heater not glow while the heating element does?
Answer:
Heat generated in a circuit is given by I2Rt. The heating element of an electric heater is made of nichrome, which has high resistance. When current flows, a large amount of heat is generated, making it red-hot and glowing. The cord of the heater is made of copper, which has very low resistance. Hence, negligible heat is produced, and it does not glow.
2. Compute the heat generated while transferring 96000 coulomb of charge in one hour through a potential difference of 50 V.
Answer:
Q = 96,000 C, t = 1 hour = 1 × 60 × 60 s = 3,600 s, V = 50 V
Heat generated, H = VQ = 50 V × 96,000 C = 4,800,000 J = 4.8 × 106 J
3. An electric iron of resistance 20 Ω takes a current of 5 A. Calculate the heat developed in 30 s.
Answer:
R = 20 Ω, I = 5 A, t = 30 s
Heat developed, H = I2Rt = 52 × 20 × 30 = 25 × 20 × 30 = 15,000 J = 1.5 × 104 J
Page 220
1. What determines the rate at which energy is delivered by a current?
Answer:
Resistance of the circuit.
2. An electric motor takes 5 A from a 220 V line. Determine the power of the motor and the energy consumed in 2 h.
Answer:
I = 5 A, V = 220 V, t = 2 h = 7,200 s
Power, P = VI = 220 × 5 = 1100 W
Energy consumed = P × t = 1100 W × 7200 s = 7,920,000 J = 7.92 × 106 J