Electricity – Concept Booster | Class 10 Science CBSE

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Home Concept Boosters CBSE CBSE Class 10 Science Electricity

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How to Use This Page

Read each concept carefully, then check the formula, common mistake, and exam tip before moving to the next. This page completely covers Electricity for CBSE Class 10 Science, explaining the invisible force that powers our modern world.

Key Concepts

Class 10 · Science · Physics

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Current Electricity

The flow of charge and its applications

Class 10 · Ch 12

Electric Current ($I$) Formula

The rate of flow of electric charge through a cross-section of a conductor. It is measured in Amperes (A) using an Ammeter, which is always connected in series.

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

Potential Difference ($V$) Formula

The work done to move a unit charge from one point to another in an electric field. Also called Voltage. It is measured in Volts (V) using a Voltmeter, which is always connected in parallel.

$$V = \frac{W}{Q}$$

Ohm’s Law Formula

At a constant temperature, the current flowing through a conductor is directly proportional to the potential difference applied across its ends.

$$V = IR \quad \text{(where } R \text{ is Resistance)}$$

Resistance ($R$) & Resistivity ($\rho$) Formula

Resistance is the opposition offered to the flow of current (measured in Ohms, $\Omega$). It depends on the length ($L$), area of cross-section ($A$), and material. Resistivity ($\rho$) is a fundamental property of the material itself.

$$R = \rho \frac{L}{A}$$

Resistors in Series Formula

Connected end-to-end. The current ($I$) is the same through all resistors, but the total voltage is the sum of individual voltage drops. Total resistance increases.

$$R_s = R_1 + R_2 + R_3 + \dots$$

Resistors in Parallel Formula

Connected between two common points. The voltage ($V$) is the same across all resistors, but the total current is the sum of branch currents. Total resistance decreases (it becomes less than the smallest individual resistor).

$$\frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \dots$$

Heating Effect (Joule’s Law) Formula

When current flows through a resistor, electrical energy is converted into heat energy. The heat produced ($H$) is directly proportional to the square of the current, the resistance, and the time.

$$H = I^2 R t$$

Electric Power ($P$) Formula

The rate at which electrical energy is consumed or dissipated in an electric circuit. Measured in Watts (W).

$$P = VI = I^2 R = \frac{V^2}{R}$$

Commercial Unit of Energy Conversion

The unit of electricity on our home electric bills is the Kilowatt-hour ($\text{kWh}$), which is called one “Unit”.

$$1 \text{ kWh} = 3.6 \times 10^6 \text{ Joules}$$

Concept Deep Dive

Resistance vs. Resistivity

The difference between an object and a material

Core Physics Concept

Resistance ($R$) belongs to the specific object you are holding. If you take a copper wire and cut it in half, its resistance decreases by half.

Resistivity ($\rho$) belongs to the material itself. It is the resistance of a perfect $1 \text{ m}^3$ cube of that substance. If you cut a copper wire in half, melt it, or stretch it, its Resistivity does not change at all. The only things that can change resistivity are changing the material (e.g., swapping copper for silver) or changing the temperature.

The Wire Stretching Trap

Volume is conserved

Crucial Understanding

A classic board question states: “A wire of resistance $10 \ \Omega$ is stretched to double its length. What is its new resistance?”

Many students quickly answer $20 \ \Omega$ ($R \propto L$). This is wrong! When you stretch a wire, you don’t add more metal. To get twice as long, it must become thinner. If Length ($L$) doubles, Area ($A$) must become half to conserve volume ($V = L \times A$).
$R_{\text{new}} = \rho \frac{2L}{A/2} = 4 \left(\rho \frac{L}{A}\right) = 4R_{\text{old}}$.
The new resistance is four times greater ($40 \ \Omega$)!

Compare & Contrast

✗ Series Circuit

Only one path for the current to flow.
If one appliance fails/breaks, the entire circuit stops working (like cheap fairy lights).
Equivalent resistance is very high, so total current drawn from the battery is low.
Voltage gets divided among the appliances.

✓ Parallel Circuit

Multiple branches/paths for the current.
If one appliance fails, the others continue to work independently (used in household wiring).
Equivalent resistance is low, so the circuit can draw high current to run powerful devices.
Every appliance gets the full source voltage (e.g., $220 \text{ V}$).

Common Mistakes to Avoid

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Mistake 1

Forgetting to Flip the Parallel Resistance: When calculating parallel resistance, students find $1/R_p = 1/2 + 1/2 = 1$. They often stop here. You MUST take the reciprocal at the end: $R_p = 1/1 = 1 \ \Omega$. If $1/R_p = 1/5$, then $R_p = 5 \ \Omega$, not $0.2 \ \Omega$!

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Mistake 2

Using Minutes in Joule’s Law: In the formula $H = I^2Rt$, Time ($t$) must strictly be in Seconds to get the answer in Joules. If the question says “for 5 minutes”, you must use $t = 300 \text{ s}$. Using $t = 5$ will completely ruin the calculation.

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Mistake 3

Placing Ammeter and Voltmeter incorrectly:
– Ammeter: Has very low resistance. Must be connected in Series so all current passes through it.
– Voltmeter: Has very high resistance. Must be connected in Parallel across the component to measure the potential drop without drawing away current.

Exam Tips

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Tip 1

The “Which Bulb is Brighter” Trick:
– If two bulbs of different powers (e.g., 40W and 100W) are connected in Parallel, the higher power (100W) bulb glows brighter (standard household setup).
– If connected in Series, the lower power (40W) bulb glows brighter because it has higher resistance, and $P = I^2R$ (Current is constant in series).

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Tip 2

V-I Graph Slope: According to Ohm’s Law ($V = IR$), the slope of a V-I graph (where V is on the Y-axis and I is on the X-axis) gives the Resistance. The steeper the line, the higher the resistance. If the axes are flipped (I-V graph), the steeper line has lower resistance!

Expected Exam Questions

Board Pattern Questions

Class 10 · Science · CBSE Exam

Class 10 · Physics

An electric refrigerator rated $400\text{W}$ operates $8\text{ hours/day}$. What is the cost of the energy to operate it for $30\text{ days}$ at Rs $3.00$ per $\text{kWh}$? [3 marks]

Answer Rs 288 📝

Explanation

1. Total power $P = 400\text{ W} = 0.4\text{ kW}$.
2. Total time $t = 8\text{ hours/day} \times 30\text{ days} = 240\text{ hours}$.
3. Electrical Energy consumed $E = P \times t = 0.4\text{ kW} \times 240\text{ h} = 96\text{ kWh}$ (or $96\text{ Units}$).
4. Total Cost $= \text{Energy} \times \text{Rate} = 96 \times 3 = \text{Rs } 288$.

Two resistors, with resistances $5\ \Omega$ and $10\ \Omega$ respectively, are connected in parallel. This combination is connected in series to a $2\ \Omega$ resistor and a $12\text{V}$ battery. Calculate the total current drawn from the battery. [3 marks]

Answer $2.25\text{ A}$ 📝

Explanation

1. First, find equivalent resistance of the parallel part ($R_p$):
$\frac{1}{R_p} = \frac{1}{5} + \frac{1}{10} = \frac{2}{10} + \frac{1}{10} = \frac{3}{10}$.
$R_p = \frac{10}{3} = 3.33\ \Omega$.
2. Now, this is in series with the $2\ \Omega$ resistor. Total Resistance ($R_{eq}$):
$R_{eq} = R_p + 2\ \Omega = \frac{10}{3} + 2 = \frac{16}{3}\ \Omega$ (or $5.33\ \Omega$).
3. Total Current $I = \frac{V}{R_{eq}} = \frac{12}{16/3} = \frac{12 \times 3}{16} = \frac{36}{16} = 2.25\text{ A}$.

Why is tungsten used almost exclusively for filament of electric lamps? [2 marks]

Answer High melting point and high resistivity at extreme temperatures. 📝

Explanation

Tungsten has an extremely high melting point ($3380^\circ\text{C}$). It can retain as much heat as possible without melting, allowing it to become “white hot” and emit brilliant light. Additionally, it does not oxidize (burn) readily at such high temperatures.

Concept Map

Electricity connects to →

Electromagnetism

Magnetic Effects of Current (Motors/Generators)

Chemical Effects (Electrolysis)

Modern Physics (Semiconductors)

Electricity – Concept Booster | Class 10 Science CBSE

Key Concepts

Current Electricity