Subject: Science

A positively charged body is said to be at positive potential or higher potential. A negatively charged body is said to be at negative potential or lower potential.

Potential difference is defined as the amount of work done in moving a unit positive charge from one point to another in an electrical circuit. The unit of p.d (V) is JC-1 which is called volt.

Potential difference (V) = IR

The e.m.f. of an electric source is the rate at which energy in a non-electrical form is converted into an electrical form during the passage of unit positive charge through it.

Voltmeter is an electrical device which measures potential difference between any two points in an electric circuit.

**Difference between emf and pd**

e.m.f | p.d. |

It is a measure of the energy supplied by a source to carry a unit charge through a circuit. | It is a measure of the work done while taking a unit charge from one point to other through a circuit. |

It is a cause of p.d. | It is an effect of e.m.f. |

It is measured in an open circuit. | It is measured in a closed circuit. |

It is greater than p.d. | It is less than e.m.f. |

The electric current passing through a conductor is directly proportional to the potential difference across its two ends at a constant physical condition. (Temperature, cross-sectional area, length, shape, nature of material etc.)

If ‘I’ is the electric current through a wire and ‘V’ is the p.d. across its ends.

I α V

V α I

V= IR………… (i) where R= electrical resistance of the conductor, which is used as constant.

From equation (i), we have

R = \(\frac{V}{R}\)

R is an electrical resistance of the conductor, which is considered as constant.

Here, I = Electric current

V = Potential difference

R = Resistance

According to the above relationship, resistance is the ratio of the potential difference across its two ends to the electric current flowing through it.

The experimental set up for the verification of the Ohm's law is shown in the figure. The given figure consists of a voltmeter (V) which is connected across a nichrome wire BC. The wire BC is connected with an ammeter (A), a key K and cells. The ammeter measure the current (I) through the circuit whereas the voltmeter measure the p.d. (V) across the wire PQ.

At first use a single cell. When the key K is closed, electric current flows in the circuit. Record the readings of the ammeter and the voltmeter. Repeat the experiment by using two cells and joining M and O. Now, join M and R and record the readings of ammeter and voltmeter. When we plott a graph between p.d (V) and current (I) and get a straight line through the origin as shown in the figure, this shows that the current indirectly proportional to the p.d. which verifies Ohm's law.

- The e.m.f. of an electric source is the rate at which energy in a non-electrical form is converted into an electrical form during the passage of unit positive charge through it.
- Voltmeter is an electrical device which measures potential difference between any two points in an electric circuit.
- According to the Ohm's law, 'The electric current passing through a conductor is directly proportional to the potential difference across its two ends at a constant physical condition.'
- Resistance is the ratio of the potential difference across its two ends to the electric current flowing through it.

- It includes every relationship which established among the people.
- There can be more than one community in a society. Community smaller than society.
- It is a network of social relationships which cannot see or touched.
- common interests and common objectives are not necessary for society.

'60 W' written in an electric bulb, 60 Joules of electrical energy is converted into heat and light energy in one second.

Before the discovery of electron, it was believed that there is the flow of positive charge from a positively charged body to a negatively charged body. This concept is still in use which is called conventional current.

But in actual practice, the direction of electron flow is the actual flow of electric current which is opposite to the conventional current.

Ammeter is an electronic device which measures the amount of current flowing through a circuit.

Voltmeter is an electronic device which measures the potential difference between any two points in a circuit.

Galvanometer is an electronic device which detects the presence of current in a circuit.

An electric circuit through which electricity flows is called a closed circuit. An electric circuit through which electricity does not flow is called a closed circuit.

- Electric bulb
- Cell
- AC source
- Switch
- Voltmeter
- Ammeter

When positive terminal of one point is connected to negative terminals of other point, it is called series combination. Similarly, when positive terminals are connected at a point and negative terminals are connected to another point, it is called parallel combination.

Ammeter is connected in series because it has low resistance and hence it measures current in the circuit without any appreciable potential drop across it.

But, voltmeter is connected in series because it has high resistance and hence it measures potential difference across the device without causing any appreciable decrease in current through a device.

But, voltmeter is connected in series because it has high resistance and hence it measures potential difference across the device without causing any appreciable decrease in current through a device.

Voltmeter is connected in parallel combination.

Potential difference is defined as the amount of work done in moving unit positive charge from one point to another in an electrical circuit. Its unit is Volt(V).

The potential difference (pd) between any two points in an electric circuit is said to be 1 V if 1 J of work is done in moving 1C charge between these two points.

Electromotive force (e.m.f) is the energy supplied by the cell per unit charge passing through the circuit. Unit of emf is volt but it is also described as the energy in joules available from the cell per coulomb of charge.

e.m.f | Pd |

It is the energy supplied by the cell per unit charge passing through the circuit. | It is the work done in moving a unit positive charge from one point to another. |

It is greater than p.d. | It is less than e.m.f. |

The property of any material to resist the flow of charges through it is called resistance. Its SI unit is ohm (Ω).

- Length of the conductor
- Cross-sectional area of the conductor
- Material of which the conductor is made
- Temperature of the conductor
- Shape of the conductor

We know that resistance of the conductor is

Combining those two relations,

R ∝

or, R = ρ

∴ ρ = .

- directly proportional to the length i.e. R ∝ ρ
- inversely proportional to its cross sectional area

Combining those two relations,

R ∝

or, R = ρ

∴ ρ = .

Ohm's law state that the current flowing through a resistor is directly proportional to the potential difference applied across it, provided the temperature and other physical conditions are constant.

i.e. I ∝ V

or, V ∝ I

or, V = IR where 'R' is the proportionality constant called resistance.

i.e. I ∝ V

or, V ∝ I

or, V = IR where 'R' is the proportionality constant called resistance.

If a current of 1 A through a conductor maintains a p.d. of 1V across its ends, then its resistance is called 1Ω.

The resistivity is the characteristics of the material of the wire. So, it does not change even if its length is tripled.

What are ohmic and non-ohmic conductor. Give an example of each.

The conductors which obey the ohm's law are known as ohmic conductor whereas those conductors which does not obey ohm's law are known as non-ohmic conductor. Example of ohmic conductor is copper and non-ohmic is semiconductor (silicon, germanium).

A number of resistors are said to be in series combination if they are joined end to end in such a way that the same current passes through each of them.

Let us consider four resistors of R1, R2, R3 and R4 are connected in series combination such that V1, V2, V3 and V4 are the pds across R1, R2, R3 and R4 respectively. The net potential difference is

V = V1 + V2 + V3 + V4

Suppose 'I' be the current in the circuit, then pd across each resistors is

V1= IR1

V2= IR2

V3= IR3

V4= IR4

So, V = IR1 + IR2 + IR3 + IR4

or, = R1 + R2 + R3 + R4

∴ R = R1 + R2 + R3 + R4

Hence, the equivalent resistor in the series is the sum of all the individual resistor in the circuit.

R = R1 + R2 + R3

V = V1 + V2 + V3 + V4

Suppose 'I' be the current in the circuit, then pd across each resistors is

V1= IR1

V2= IR2

V3= IR3

V4= IR4

So, V = IR1 + IR2 + IR3 + IR4

or, = R1 + R2 + R3 + R4

∴ R = R1 + R2 + R3 + R4

Hence, the equivalent resistor in the series is the sum of all the individual resistor in the circuit.

R = R1 + R2 + R3

If the number of resistors are connected across the same potential, then it is said to be in parallel combination.

Let us consider four resistance, R1, R2, R3 and R4 connected in parallel such that current through each is I1 , I2, I3, I4

Here, total current will be I = I1 + I2 + I3+ I4 If V be the potential across each resistor I1 = , I2 = , I3 = , I4 = and

Now,

I = V (+ + +)

or, = V (+ + +)

or, = + + +

Hence, the equivalent resistance in parallel combination

= + + + ....................+

Here, total current will be I = I1 + I2 + I3+ I4 If V be the potential across each resistor I1 = , I2 = , I3 = , I4 = and

Now,

I = V (+ + +)

or, = V (+ + +)

or, = + + +

Hence, the equivalent resistance in parallel combination

= + + + ....................+

The name of instruments X and Y are ammeter and voltmeter respectively. Here, in figure, R is resistance and K is key. The direction of current flow is:

Current (I) = 1A

Time (t) = 30 min = 30 x 60 sec = 1800 sec

Charge (Q) = ?

Now,

By using formula,

I =

or, Q = I x t

= 1800 x 1

= 1800 C

Hence, 1800 C charge flows through the circuit.

Here,

Length (= 5m

Resistance (R) = 2Ω

Area (A) = 0.1 m^{2}

Resistivity (ρ) = ?

Conductivity (σ) = ?

Now,

ρ = = = 0.04Ωm

And conductivity( σ) = = 1/0.04 = 25m/ohm

Resistance (R) = 20Ω

Current (I) = 0.25A

Pd of battery (V) = ?

Using ohm's law,

V = IR

or, V = 0.25 x 20

or, V = 5 V

Hence, the pd required to the battery is 5V.

Current (I) = 0.25A

Pd of battery (V) = ?

Using ohm's law,

V = IR

or, V = 0.25 x 20

or, V = 5 V

Hence, the pd required to the battery is 5V.

Potential difference (V) = 30V

Current (I) = 5A

Resistance (R) = ?

By ohm's law,

V = IR

or, R = = = 6Ω

Hence, 6Ω resistance is occurred between these two points.

Current (I) = 5A

Resistance (R) = ?

By ohm's law,

V = IR

or, R = = = 6Ω

Hence, 6Ω resistance is occurred between these two points.

Given,

First resistance (R1) = 50Ω

Another resistance (R2) = 10Ω

Equivalent resistance (R) = ?

Current (I) = ?

Pd supply (V) = 12 V

As we know that, in series connection

R = R1 + R2

= 50 + 10

= 60Ω

Now, using Ohm's law,

V = IR

or, I =

or, I =

or, I = 0.2 A

Hence, equivalent resistance is 60Ω and current is 0.2A.

First resistance (R1) = 50Ω

Another resistance (R2) = 10Ω

Equivalent resistance (R) = ?

Current (I) = ?

Pd supply (V) = 12 V

As we know that, in series connection

R = R1 + R2

= 50 + 10

= 60Ω

Now, using Ohm's law,

V = IR

or, I =

or, I =

or, I = 0.2 A

Hence, equivalent resistance is 60Ω and current is 0.2A.

Given,

Power of heater (P) = 1000 W

Pd applied (V) = 220V

Current (I) = ?

By using formula,

P = I x V

or, 1000 = I x 220

or, I =

= 4.54 A

Hence, 4.54 A current flows through a heater.

Power of heater (P) = 1000 W

Pd applied (V) = 220V

Current (I) = ?

By using formula,

P = I x V

or, 1000 = I x 220

or, I =

= 4.54 A

Hence, 4.54 A current flows through a heater.

Given,

Power of bulb (P) = 100 W

Pd supplied (V) = 220 V

Resistance of bulb (R) = ?

We know that,

P = I x V

or, I = = 0.45 A

Similarly, by using ohm's law,

V = IR

or, 220 = 0.45 x R

or, R = 220/0.45

or, R = 488.89 Ω

Hence, the resistance nearly 889Ω.

Power of bulb (P) = 100 W

Pd supplied (V) = 220 V

Resistance of bulb (R) = ?

We know that,

P = I x V

or, I = = 0.45 A

Similarly, by using ohm's law,

V = IR

or, 220 = 0.45 x R

or, R = 220/0.45

or, R = 488.89 Ω

Hence, the resistance nearly 889Ω.

- Name the instruments X and Y.
- Why is Y connected in that way?
- Find the value that Y measures if pd is 20V.

Here,

Here, X is voltmeter and Y is ammeter.

Y is connected in that way because it has low resistance and has no applicable loss of current.

Pd (V) = 20V

Resistance (R) = 3Ω

So, current that is measured by Y (I) = ?

Using V = IR,

I = = = 6.67A

Hence, Y instrument measures 6.67 A.

Here, X is voltmeter and Y is ammeter.

Y is connected in that way because it has low resistance and has no applicable loss of current.

Pd (V) = 20V

Resistance (R) = 3Ω

So, current that is measured by Y (I) = ?

Using V = IR,

I = = = 6.67A

Hence, Y instrument measures 6.67 A.

Calculate the current through a conductor when 200C charge flows through in it in 25 seconds.

Here

Charge (Q) = 200C

Time (t) = 25s

Current (I) = ?

We have,

I = \(\frac{Q}{t}\)

= \(\frac{200}{25}\)

= 8A.

Therefore, the current through the conductor is 8A.

Study the following figure to answer the questions:

(i). Name the instruments P and Q.

(ii). In an experiment if p.d. across R is 2.4V and R= 0.8Ω , what will be the current through the circuit?

(i). In the given, the instruments P is voltmeter. The instruments Q is ammeter.

(ii). V = 2.4

R =0.8Ω

Current (I) = ?

By Ohm,s law,

V = IR.

\(\therefore\) 2.4 = I (0.8)

OR,

I = \(\frac{2.4}{0.8}\)

= 3A

Therefore, the current through the circuit is 3A.

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