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NCERT Resistors Science Chapter Class 10

Ohm’s Law:

The current flowing through the conductor is directly proportional to the potential difference across the ends of the conductor provided its temperature and other physical conditions remain the same.

Mathematically,

V ∝ I

V = RI

R = Resistance of the conductor, constant

Slope=V₂ - V₁/ I₂ - I₁

= Δ V/ ΔI

=Resistance

Slope of V and I graph - gives resistance of the conductor.

= Δ V¹/ ΔI¹ > Δ V²/ ΔI²

=R¹ > R²

Resistance:

The property of conductor which opposes the flow of charge through the conductor.

R = V/I

1ohm = 1 volt/1 Ampire

1 = 1 V/A

R ∝ l, R∝1/A

Factors on which resistance of conductor depends:

Length of conductor
Area of cross section
Nature of Material
Temperature

Resistivity:

Experimentally it has been found that:

R ∝ l

R ∝ 1/A

R = l/A

= Resistivity , specific resistance of conductor.

Let us consider 3 resistors r₁, r₂, r₃ are connected in series. Lets take v be the potential difference applied to all the resistors. Let us take v₁, v₂, v₃ be the potential difference across the resistors r₁, r₂, r₃ respectively. Let I be the current flowing through each resistors.

V= v₁ + v₂ + v₃

V = IR₁ + IR₂ + IR₃

If R₃ be the equivalent resistance of the circuit , then V = IR₁

So, IR₁ = IR₁ + IR₂ + IR₃

R₁ = R₁ + R₂ + R₃ Resistivity is numerically equal to the resistance offered by a cube of that material having length 1m and area of cross section 1m²

8. A copper wire has dimension 1 cm x 1 cm x 50 cm, if it has resistivity 2.82 x 10^-6, then findout the resistance between 2 square faces of conductor. Ans: R = l/A = 2.82 x 10-6 x s/10 = 1.41 x 10^-2 Combination of resistors: Series combination Current – same Potential difference - divided

When 2 or more resistors are joined end to end such that the same current will flow through each resistor and the potential is divided separately across each resistor then the connection is known as series connection.

In case of series connection the equivalent connection increases.

Let us consider 3 resistors r₁, r₂, r₃ are connected in parallel. Let us consider v be the potential difference applied to all the resistors. if I₁, I₂, I₃ be the current flowing through R₁, R₂, R₃ respectively, then we have

I = I₁ + I₂ + I₃

V/R = V/R₁ + V/R₂ + V/R₃

1/R = 1/R₁ + 1/R₂ + 1/R₃

In case of series connection if one appliances will be damaged, the circuit will not work.

If n no of resistors of resistance R are joined in series then the equivalent resistance will be

R_s = R₁ + R₂ + R₃ + …..+ R_n
=R + R +….
=nR

In case of series connection the resistance increases as the length increases.

Parallel connection:

If the common end of 3 resistors are joined to one terminal of the source and other ends are joined to the other terminal such that the same potential difference can be applied to each resistors and current will be divided across each resistor.