Question

Where will length half and area doubled. In a 4ohm resistance wire is doubled on it calculate the new resist of the wire

Answer 1

The resistance doesn't change.... because area is 2 time and length is become half

Answer 2

GIVEN:—

$\boxed{ \pink \bigstar \sf R_{resistance} = 4 \Omega = \dfrac{ \rho \: l}{A }}$

• Here l represent length of wire
• A represent area of cross section.

TO FIND OUT:—

$\red \bigstar \sf \: R _{new} = {?}$

SOLUTION:—

As the length of the wire is halved and the area is doubled.

• New length =l/2
• New area =2A

✮According to question

$\leadsto \boxed{\sf \: R _{new} = \dfrac{ \rho \frac{l}{2} }{2A} }$

$\leadsto \boxed{\sf \: R _{new} = \dfrac{1}{4} \bigg(\dfrac{ \rho l }{A} \bigg)}$

$\leadsto \boxed{\sf \: R _{new} = \dfrac{1}{4} \times 4} \: \: \: \: \: \: | \sf \: given \: |$

$\leadsto \boxed{\boxed{\sf \red{ \: R _{new} = 1 \Omega} }}$

New resistance of the wire is 1 ohm .

More to know :-

• Resistivity of a material is defined as resistance offered by a cylinder or a cube of one metre² and one metre when current flows perpendicular to the opposite end of it.
• Resistivity depends on the nature of the material of the conductor and also om Temperature.
• Unit of Resistivity is ohm m or ohm cm.
• Different elements have different Resistivity. Silver has lowest Resistivity 1.6×10-⁸ while nichrome has the highest 100×10-⁸.Thus silver us good conductor of electricity while nichrome is bad conductor of electricity.

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