Lecture-2 : CLASS-X: SCIENCE : Chapter: Electricity Content: numericals

NUMERICAL PROBLEMS ON ELECTRICITY; CLASS 10

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Q1. How much work is done in moving a charge of 3 coulombs from a point at 110 volts to a point at 220 volts?

Soln. We know, 

Potential difference = work done/charge moved

or.          V   =   W/Q

∴   W =  VQ

Here, potential difference, V = 220 - 110 = 110 volts and Charge moved , Q = 3 coulombs

 ∴  W = VQ = 3 x 110 joules = 330 joules

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Q2. How much energy is given to each coulomb of charge passing through a 6 volt battery?

Soln. We know, 

Potential difference = work done/charge moved

or.          V   =   W/Q

∴   W =  VQ

Here, potential difference, V = 6 volts

and charge Q = 1 coulomb ( each coulomb given)

∴   W =  VQ = 6 x 1 joules = 6 joules

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Q3. What is the potential difference between the terminals of a battery if 500 joules of work is required to transfer 25 coulombs of charge from one terminal of battery to the other?

Soln. We know, 

Potential difference = work done/charge moved

or.          V   =   W/Q

Workdone , W = 500 joules

Charge moved, Q = 25 coulombs

∴  V   =   W/Q = 500/25 = 20 volts

Therefore, the potential difference between the terminals of the battery = 20 volts

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Q4. A circuit contains a battery of 1.4 V with a resistance of 2 ohms and a resistance of 5 ohms connected in series. Calculate the current flowing through the circuit and the potential difference across the 5 ohm resistance.

Using Ohm's law, we can calculate the current flowing through the circuit as:

I = V / R_total

where V is the voltage of the battery, and R_total is the total resistance of the circuit, which is the sum of the resistance of the 2-ohm resistor and the 5-ohm resistor:

R_total = R₁ + R₂ = 2 ohms + 5 ohms = 7 ohms

So we have:

I = 1.4 V / 7 ohms = 0.2 A

Therefore, the current flowing through the circuit is 0.2 A.

To calculate the potential difference across the 5 ohm resistor, we can use Ohm's law again, using the current we just calculated:

V_5ohm = I * R₂

where R₂ is the resistance of the 5 ohm resistor. Substituting the values we have:

V_5ohm = 0.2 A * 5 ohms = 1 V

Therefore, the potential difference across the 5 ohm resistor is 1 V.

Q5. A parallel circuit contains two resistors, one with a resistance of 10 ohms and the other with a resistance of 20 ohms. If the voltage across the circuit is 12 volts, calculate the total current flowing through the circuit and the current through each resistor.

Q6. An electric motor is rated at 120 volts and draws a current of 5 amperes. Calculate the power consumed by the motor.

Q7. A 220-volt electric heater draws a current of 5 amperes. Calculate the resistance of the heater.

Q8. A circuit contains a 10-ohm resistor, a 5-ohm resistor, and a 12-volt battery. Calculate the total current flowing through the circuit and the potential difference across each resistor.

Q9. An electric power station produces 1000 megawatts of power. If the voltage of the power lines is 100,000 volts, calculate the current flowing through the lines.

Q10. A transformer has a primary coil of 100 turns and a secondary coil of 500 turns. If the primary coil is connected to a 240-volt power source, calculate the voltage across the secondary coil.