## Numerical Problems on Electricity Class 10

Q1. How much work is done when one coulomb charge moves against a potential difference of 1 volt ?

Ans: 1 J

Q2. How much work is done in moving a charge of 2 C across two points having a potential difference of 12 V ?

Ans: 24 joules.

Study Material: Click Material

Q3. Calculate the work done in moving a charge of 4 coulombs from a point at 220 volts to another point at 230 volts.

Ans: 40 joules

Q4. How much energy is transferred by a 12 V power supply to each coulomb of charge which it moves around a circuit ?

Ans: 12 joules.

Q5. What is the potential difference between the terminals of a battery if 250 joules of work is required to transfer 20 coulombs of charge from one terminal of battery to the other ?

Ans: 12.5 V

Q6. Three 2 V cells are connected in series and used as a battery in a circuit.

(a) What is the p.d. at the terminals of the battery ?

(b) How many joules of electrical energy does 1 C gain on passing through (i) one cell (ii) all three cells ?

**Ans: **(a) 6V (b) (i) 2 joules (ii) 6 joule.

**Question 7:**

(a) How many milliamperes are there in 1 ampere ?

(b) How many microamperes are there in 1 ampere ?**Solution :**

(a) 1 amp = 10^{3} milli amp.

(b) 1 amp = 10^{6} micro amp.

Q8. If 20 C of charge pass a point in a circuit in 1 s, what current is flowing ?

Ans: 20 A.

Q9. A current of 4 A flows around a circuit for 10 s. How much charge flows past a point in the circuit in this time ?

Ans: 40 C

Q10. What is the current in a circuit if the charge passing each point is 20 C in 40 s ?

Ans: 0.5A

Q11. If a potential difference of 10 V causes a current of 2 A to flow for 1 minute, how much energy is transferred ?

Ans: 1200 J

Q12. A radio set draws a current of 0.36 A for 15 minutes. Calculate the amount of electric charge that flows through the circuit.

Ans: 324 C

Q13. If the charge on an electron is 1.6 x 10^{-19} coulombs, how many electrons should pass through a conductor in 1 second to constitute 1 ampere current ?

Ans:

Q14. The p.d. across a lamp is 12 V. How many joules of electrical energy are changed into heat and light when :

(a) a charge of 1 C passes through it ?

(b) a charge of 5 C passes through it ?

(c) a current of 2 A flows through it for 10 s ?**Solution :**

Q15. In 10 s, a charge of 25 C leaves a battery, and 200 j of energy are delivered to an outside circuit as a result.

(a) What is the p.d. across the battery ?

(b) What current flows from the battery ?**Solution :**

Q16. A flash of lightning carries 10 C of charge which flows for 0.01 s. What is the current ? If the voltage is 10 MV, what is the energy ?

Ans:

Q17. An electric heater is connected to the 230 V mains supply. A current of 8 A flows through the heater.

(a) How much charge flows around the circuit each second ?

(b) How much energy is transferred to the heater each second ?

Solution:

Q18. How many electrons are flowing per second past a point in a circuit in which there is a current of 5 amp ?**Solution :**

Q19. A potential difference of 20 volts is applied across the ends of a resistance of 5 ohms. What current will flow in the resistance ?

Ans: 4 A

Q20. A resistance of 20 ohms has a current of 2 amperes flowing in it. What potential difference is there between its ends ?

Ans: 40 V

Q21. A current of 5 amperes flows through a wire whose ends are at a potential difference of 3 volts. Calculate the resistance of the wire.

Ans: 0.6 ohm

Q22. When a 12 V battery is connected across an unknown resistor, there is a current of 2.5 mA in the circuit. Calculate the value of the resistance of the resistor.

Ans: 4800 ohm.

Q23. What p.d. is needed to send a current of 6 A through an electrical appliance having a resistance of 40 Ω ?

Ans: 240 V.

Q24. The potential difference between the terminals of an electric iron is 240 V and the current is 5.0 A. What is the resistance of the electric iron ?

Ans: 48 ohm.

Q25. An electric room heater draws a current of 2.4 A from the 120 V supply line. What current will this room heater draw when connected to 240 V supply line ?

Ans: 4.8 amp

Q26. A p.d. of 10 V is needed to make a current of 0.02 A flow through a wire. What p.d. is needed to make a current of 250 mA flow through the same wire ?

Ans: 125 volt.

Q27. A current of 200 mA flows through a 4 kΩ resistor. What is the p.d. across the resistor ?

Ans: 800 volt.

Q28. What will be the resistance of a metal wire of length 2 m and area of cross-section 1.55 × 10^{-6} m^{2}, if the resistivity of the metal be 2.8 × 10^{-8} Ωm ?

S**olution :**

Q29. Calculate the resistance of a copper wire 1.0 km long and 0.50 mm diameter if the resistivity of copper is 1.7 × 10^{-8} Ωm.**Solution :**

Q30. Calculate the resistance of an aluminium cable of length 10 km and diameter 2.0 mm if the resistivity of aluminium is 2.7 x 10^{-8}Ωm.

**Solution :**

Q31. How does the resistance of a wire change when :

(i) its length is tripled ?

(ii) its diameter is tripled ?

(in) its material is changed to one whose resistivity is three times ?

Solution:

Q32. Calculate the area of cross-section of a wire if its length is 1.0 m, its resistance is 23 Ω and the resistivity of the material of the wire is 1.84 x 10^{-6} Ωm.**Solution :**

Q33. A piece of wire of resistance 20 Ω is drawn out so that its length is increased to twice its original length. Calculate the resistance of the wire in the new situation.

Solution:

Q34. If 3 resistances of 3 ohm each are connected in parallel, what will be their total resistance ?**Solution :**

Q35. Show how you would connect two 4 ohm resistors to produce a combined resistance of

(a) 2 ohms

(b) 8 ohms.**Solution :**

(a) By connecting in parallel: Since equivalent resistance will be

1/ R = 1/4 + 1/4 = 2/4 = 1/2

Therefore, R = 2 ohm

(b) By connecting in series : Since equivalent resistance will be

R = 4 ohm + 4 ohm = 8 ohm.

Q36. Which of the following resistor arrangement, A or B, has the lower combined resistance ?

**Solution :**

Resistance of arrangement A is 10 ohm.

Combined resistance of arrangement B is caculated as follows:

1/R = 1/10 + 1/1000 = (100+1)/1000

R = 1000/101 = 9.9 ohm

Therefore, arrangement B has lower combined resistance.

Q37. A wire that has resistance R is cut into two equal pieces. The two parts are joined in parallel. What is the resistance of the combination ?**Solution :**

Resistance of each part is R/2.

Resultant resistance R’ is given by

1/R’ = 2/R+2/R

R’=R/4.

Q38. Calculate the combined resistance in each case :

**Solution :**

Q39. Find the current in each resistor in the circuit shown below :

**Solution :**

Q40. For the circuit shown in the diagram below :

What is the value of :

(i) current through 6 Ωresistor ?

(ii) potential difference across 12 Ω resistor ?**Solution :**