# Frank Solutions for Chapter 4.1 Ohm's Law and Electrical Circuits Class 10 Physics ICSE

**Exercises**

**1. What do you mean by a cell?**

**Answer**

An electric cell is a device in which a constant difference in potential is maintained between the two conductors by a chemical reaction. Thus, a cell can be used as a source of electrons or current. In a cell, chemical energy changes into electrical energy when it is in use.

**2. What is the difference between a cell and a battery?**

**Answer**

An electric cell produces electricity from the chemicals stored inside it. When the chemicals in the electric cell are used up, the electric cell stops producing electricity. It has two terminals - positive and negative.

When two or more cells are connected together such that the positive terminal of one cell is connected to the negative terminal of the next cell; such a combination of two or more cells is called a battery. A battery is thus a combination of two or more cells.

**3. What do you understand by an electric circuit?**

**Answer**

An electrical circuit is a continuous path comprising of conducting wires and resistances between the terminals of a battery, along which an electric current is set up. It is represented by drawing a circuit diagram.

**4. Name any four components of an electric circuit. Write their symbols also.**

**Answer**

Four components of an electrical circuit :

**5. What do you mean by a circuit diagram?**

**Answer**

A diagram indicating how various components in an electrical circuit have been connected using symbols for those components is a circuit diagram.

**6. What is wrong with the circuit diagram (Fig. 34)? Carefully check the symbols and assign proper positive and negative signs to them.**

**Answer**

In the given diagram, ammeter is connected in parallel and voltmeter in series, which is wrong. Also the terminals of the two devices are wrongly connected to the battery.

Correct diagram:

Correct diagram:

**7. State Ohm's law. Is it always true?**

**Answer**

According to Ohm's law, the current flowing in a conductor is directly proportional to the potential difference across its ends provided the physical conditions and temperature of conductor remains constant.

No, it is not always true. E.g. Diode valve, junction diode etc. do not obey Ohm's law.

No, it is not always true. E.g. Diode valve, junction diode etc. do not obey Ohm's law.

**8. What is electrical resistance? Write its SI unit.**

**Answer**

The obstruction offered to the flow of current by the wire is called its electrical resistance. It is a kind of friction between the free electrons and the atoms of the conductor along which they flow.

Its SI unit is 'ohm'.

Its SI unit is 'ohm'.

**9. Name the physical quantity that represents the ratio of potential difference and current.**

**Answer**

The physical quantity is 'resistance'.

**10. Define one ohm.**

**Answer**

Resistance of a conductor is said to be 1 ohm, if 1 ampere current flows through it, when the potential difference across its ends is 1 volt.

**11. Does Ohm's law hold good for semiconductors and electrolytic solutions?**

**Answer**

No, Ohm's law does not hold good for semiconductors and electrolytic solutions.

**12. State the factors on which the resistance of a conductor depends.**

**Answer**

Factors on which the resistance of a conductor depends are:

- Nature of conductor: different materials have different concentration of free electrons and therefore resistance of a conductor depends on its material.
- Length of conductor: Resistance of a conductor is directly proportional to the length of a conductor.
- Area of cross-section of a conductor: Resistance of a conductor is inversely proportional to the area of cross-section of the uniform wire.
- Temperature of conductor: In general for metallic conductors, higher the temperature larger is the resistance.

**13. What do you mean by an equivalent resistance?**

**Answer**

An equivalent resistor is that resistor which when replace any combination of resistors the current through the circuit is not altered or changed.

**14. A simple electric circuit has 24 V battery and a resistor of 60 Î©. What will be the current in the circuit ? The resistance of the connecting wires is negligible .**

**Answer**

Current = Potential difference (V)/Resistance (R)

Here, V = 24 volt, R = 60 Î©

∴ Current = 24/60 = 0.4 A

Here, V = 24 volt, R = 60 Î©

∴ Current = 24/60 = 0.4 A

**15. A graph is plotted taking p.d. along y - axis and electric current along x - axis. Name the physical quantity that represents the slope of this graph (Fig. 35).**

**Answer**

The slope of the graph (dV/dI) gives the value of resistance.

**16. Define resistivity of a metal.**

**Answer**

The resistivity of a material is the resistance of a wire of that material of unit length and unit area of cross-section.

**17. What are the SI units of specific resistance?**

**Answer**

The SI unit of specific resistance is ohm-metre (â„¦m).

**18. What do you mean by conductance of a conductor?**

**Answer**

Conductance of a conductor is the reciprocal of resistance of that conductor. Its unit is mho.

**19. Name the following substances:**

**(i) Showing low resistivity,**

(ii) Showing very high resistivity,

(iii) Showing moderate resistivity.

(ii) Showing very high resistivity,

(iii) Showing moderate resistivity.

**Answer**

(i) Metals e.g. copper

(ii) Alloys e.g. Constantan

(iii) Semiconductors e.g. Germanium

(ii) Alloys e.g. Constantan

(iii) Semiconductors e.g. Germanium

**21. State the law which relates the current in a conductor to the potential difference across its ends.**

**Answer**

Ohm's law relates the current in a conductor to the potential difference across its ends.

According to Ohm's law, the current flowing in a conductor is directly proportional to the potential difference across its ends provided the physical conditions and temperature of conductor remains constant.

According to Ohm's law, the current flowing in a conductor is directly proportional to the potential difference across its ends provided the physical conditions and temperature of conductor remains constant.

**22. What happens to the resistance if the conductor is made thinner?**

**Answer**

If the conductor is made thinner, electrons get smaller area of cross-section to flow and it therefore, offers a large resistance.

**23. What kind of plot would you except when current (I) is plotted against potential difference (V) for a conductor, at constant temperature?**

**Answer**

At constant temperature, if current is plotted against potential difference, the plot will be a straight line making some slope with the x-axis as shown in figure below:

**24. What is an ammeter? How is it connected in a circuit?**

**Answer**

The instrument used to measure electric current is called an ammeter. It has a low resistance and is always connected in series.

**25. What is a voltmeter? How is it connected in a circuit?**

**Answer**

The instrument used to measure electric potential or potential difference is called a voltmeter. It has a very high resistance and is always connected in parallel.

**26. Does an ammeter have a low or high resistance?**

**Answer**

An ammeter has a low resistance.

**27. Does a voltmeter have a low or high resistance?**

**Answer**

A voltmeter has a high resistance.

**28. What is the role of a key in an electric circuit?**

**Answer**

A key acts as a switch in an electric circuit. It helps to open or close the circuit as required.

**29. What do you mean by a rheostat?**

**Answer**

A rheostat is a device used in electric circuit to regulate current without changing the voltage source. It is also called variable resistance.

**30. A simple electric circuit has a 30 V battery and a resistor at 60 â„¦. What will be the current in the circuit ? The resistance of the connecting wires is negligible.**

**Answer**

A/c to Ohm's law,

I = V/R

Here, V = 30 volt and R = 60 â„¦

∴ I = 30/60 = 0.5 A

I = V/R

Here, V = 30 volt and R = 60 â„¦

∴ I = 30/60 = 0.5 A

**31. Potential difference between two points of a wire carrying 2 ampere current is 0.1 volt. Calculate the resistance between these points.**

**Answer**

A/c to Ohm's law,

R = V/I

Here, V = 0.1 volt and I = 2A

Here, V = 0.1 volt and I = 2A

∴ R = 0.1/2 = 0.05 â„¦

**32. The potential difference between the terminals of an electric iron is 240 V and the current flowing through it is 6 A. What is the resistance of the electric iron?**

**Answer**

A/c to Ohm's law,

R = V/I

Here, V = 240 volt and I = 6A

Here, V = 240 volt and I = 6A

∴ R = 240/6 = 40 â„¦

Thus, the resistance of the electric iron is 40â„¦

Thus, the resistance of the electric iron is 40â„¦

Given , potential difference, V = 2 volt

Let R be the equivalent resistance of the circuit and I be the current flowing through it; then:

Let R be the equivalent resistance of the circuit and I be the current flowing through it; then:

**34. What potential difference is needed to drive a current of 1 A through a 5 â„¦ resistor ?**

**Answer**

Let the required potential difference be V.

Given, current I = 1 A and Resistance, R = 5 â„¦

A/C to Ohm's law,

V = IR = (1)× (5) = 5 volt

Given, current I = 1 A and Resistance, R = 5 â„¦

A/C to Ohm's law,

V = IR = (1)× (5) = 5 volt

**35. A potential difference of 6 V is applied across at 3â„¦ resistor. What is the current flowing through the circuit ?**

**Answer**

Let I be the current flowing through it

Given, potential difference, V = 6 volt and Resistance, R = 3â„¦

Given, potential difference, V = 6 volt and Resistance, R = 3â„¦

A/C to Ohm's law,

I = V/R = 6/3 = 2A

I = V/R = 6/3 = 2A

**36. What is the value of a resistance if 20 V drives 2 A through it?**

**Answer**

A/C to Ohm's law,

R = V/I = 20/2 = 10 â„¦

R = V/I = 20/2 = 10 â„¦

**Answer**

Between A and B, the series combination of two resistors of resistances 2 ohm each is connected in parallel with the 1 ohm resistor.

∴ Equivalent series resistance between A and B, R = 2+2 = 4 â„¦

Now, between A and B this 4â„¦ resistor is connected in parallel with 1 â„¦ resistor.

∴Equivalent resistance between A and B,

∴ Equivalent series resistance between A and B, R = 2+2 = 4 â„¦

Now, between A and B this 4â„¦ resistor is connected in parallel with 1 â„¦ resistor.

∴Equivalent resistance between A and B,

**38. What is the equivalent resistance of 5 equal resistors, each of value 2 â„¦, when connected in (a) Series, (b) Parallel ?**

**Answer**

**39. How will you connect five resistors, each of the value one ohm, to obtain an equivalent resistance of 0.2â„¦?**

**Answer**

Five resistors each of value 1 ohm should be connected in parallel to obtain an equivalent resistance of 0.2 ohm.

**40. Give two uses of conductors.**

**Answer**

Two uses of conductors:

- Connecting wires are made of conductors like copper.
- Conductors are used as electrolytes in cells

**41. Write the SI units for:**

**(a) Electric current (b) Potential difference**

(c) Charge.

(c) Charge.

**Answer**

(a) Ampere

(b) Volt

(c) Coulomb

(b) Volt

(c) Coulomb

**42. Define potential difference between two points.**

**Answer**

The potential difference between two points may be defined as the work done in moving a unit positive charge from one point to the other.

**43. Is electric potential a scalar or a vector physical quantity?**

**Answer**

Electrical potential is a 'scalar' quantity.

**44. Define electric intensity. Write its SI unit. Is it a scalar or a vector physical quantity?**

**Answer**

Electric intensity is defined as the force experienced by a unit positive charge when kept at that point.

Its SI unit is newton per coulomb. It is a vector quantity.

Its SI unit is newton per coulomb. It is a vector quantity.

**45. By what name is the unit joule/coulomb called?**

**Answer**

Joule/coulomb is known as 'volt'.

**46. How much work is done when 5 C charge moves across a p.d. of 1 V?**

**Answer**

Work done = charge x potential difference

Or, W = 5×1 = 5 J

Or, W = 5×1 = 5 J

**47. The work done in moving unit positive charge across two points in an electric circuit is a measure of**

(i) Current

(ii) Potential difference

(iii) Resistance

(iv) Power

(i) Current

(ii) Potential difference

(iii) Resistance

(iv) Power

**Answer**

(ii) potential difference

**48. The device used for measuring potential difference is**

(i) Potentiometer

(ii) Ammeter

(iii) Galvanometer

(i) Potentiometer

(ii) Ammeter

(iii) Galvanometer

**Answer**

(iv) voltmeter

**49. What are the conditions under which charges can move in a conductor?**

**Answer**

Charges move in a definite direction in a conductor when a potential difference is applied across the ends of the conductor.

**50. How will you maintain a potential difference between the ends of a conductor?**

**Answer**

We can maintain a potential difference between the ends of a conductor by connecting the two ends of the conductor to the two terminals of a battery or cell.

**51. What do you mean by electric current?**

**Answer**

The rate of movement of charge from one point to another through a section of the conductor is called electric current. Current refers to rate of flow of charges in a conductor.

I = Q/t

I = Q/t

**52. What is the direction of electric current?**

**Answer**

The direction of conventional current is taken as the direction of flow of positive charges.

The direction of electronic current is taken as opposite to the direction of motion of electrons.

The direction of electronic current is taken as opposite to the direction of motion of electrons.

**53. Name the physical quantity which defines the rate of flow of charge.**

**Answer**

Current defines the rate of flow of charges in a conductor.

**54. Name the physical quantity which is measured by an ammeter.**

**Answer**

Current is measured by an ammeter.

**56. A battery of e.m.f. 15 V and internal resistance 3 ohm is connected to two resistors of resistance 3 ohm and 6 ohm in series. Find:**

**(i) The current through the battery,**

(ii) The p.d. between the terminals of the battery.

(ii) The p.d. between the terminals of the battery.

**Answer**

Given, emf, e = 15 v

Internal resistance, r = 3 â„¦

Internal resistance, r = 3 â„¦

(ii) Potential difference = emf - voltage drop = e - (Ir)

Now, voltage drop = current × internal resistance = 1.25 × 3 = 3.75

∴ p.d. = 15 - 3.75 = 11.25 V

**57. A wire of uniform thickness with a resistance of 27 â„¦ is cut into three equal pieces and they are joined in parallel. Find the resistance of the parallel combination.**

**Answer**

When a wire of uniform thickness with resistance 27 ohm is cut into three equal pieces, the resistance of each piece = 27/3= 9ohm.

Now, equivalent resistance of three 9 ohm resistors connected in parallel is :

Now, equivalent resistance of three 9 ohm resistors connected in parallel is :

**58.**

**You have three resistors of values 2 â„¦, 3â„¦, and 5â„¦. How will you join them so that the total resistance is less than 2 â„¦ ?**

**Answer**

To get a total resistance less than 2 ohm, the given resistors should be connected in parallel because in parallel combination the equivalent resistance is less than the resistance smallest connected resistor.

**59. Calculate the equivalent resistance of the following combination of resistor r**

_{1}, r_{2}, r_{3}and r_{4}.**Answer**

In the given network, the series combination of resistors, r

_{1 }and r_{2}, is connected in series with the parallel combination of resistors, r_{3}and r_{4}.