Physics, asked by lachunanda926, 7 months ago

A 6ohm resistance wire is doubled on itself . Calculate the new resistance of the wire itself .​

Answers

Answered by Bᴇʏᴏɴᴅᴇʀ
12

Answer:-

\red{\bigstar} New Resistance \large\leadsto\boxed{\rm\purple{1.5 \Omega}}

Given:-

Resistance = 6 Ω

Wire is doubled on itself.

To Find:-

New resistance of the wire.

Solution:-

We know,

\red{\bigstar}\large\boxed{\sf\green{R = \rho \dfrac{l}{A}}}

here,

R = resistance

p = resistivity of wire

l = length of the wire

A = area of cross section of the wire.

Substituting in the value:-

\sf{6 = \rho \dfrac{l}{A}}

Given that, the wire is doubled.

hence,

• New Area A' = 2A

Now, the area is doubled therefore the length of the wire will become half.

• New length l' = l/2

Substituting in the Formula:-

\sf{R' = \rho \dfrac{\frac{l}{2}}{2A}}

\sf{R' = \rho \dfrac{l}{2 \times 2A}}

\sf{R' = \rho \dfrac{l}{4A}}

\sf{R' = \dfrac{1}{4} \bigg(\rho \dfrac{l}{A}\bigg)}

\sf{R' = \dfrac{1}{4} \bigg(R \bigg) \: \: \: \: \: \: \: \bigg(\because R = \rho \dfrac{l}{A}\bigg)}

\sf{R' = \dfrac{1}{4} \times 6 \: \: \: \: \: \: \: \bigg(\because R = 6 \bigg)}

\sf{R' = \dfrac{3}{2}}

\large\bf\pink{R' = 1.5 \Omega}

Therefore, the new resistance of the wire will be 1.5Ω .

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