A 40Ω resistor is to be wound from platinum wire 0.1mm in diameter.How much wire is needed ? Given ( ρ = 11×10⁻⁸ Ωm )

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A 40 ohm resistor is to be wound from platinum wire 0.1mm in diameter.How much wire is needed ? Given (resistivity ρ = 11×10⁻⁸ Ωm )  Physics class 12 problem solution  Inter class physics problem solution

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00:00Question is, a 40 ohm resistor is to be wound from platinum wire 0.1 mm in diameter, how

00:16much wire is needed as resistivity of platinum is obtained is 11 into 10 raised power minus

00:248 ohm meter. So, first of all, we will make a data. The resistance is obtained as 40 ohm

00:44and diameter is obtained as 0.1 mm. As we know that, diameter is obtained as 2r. So, r will

01:00be equal to d upon 2. So, diameter is obtained as 0.1 mm divided by 2. So, radius will be

01:15obtained as 0.1 divided by 2. It will be 0.05 mm. So, radius will be obtained as 0.05 into

01:291 mm is equal to 10 raised power minus 3 meter. So, we have to find the length of wire.

01:46amoser resistance resistivity is obtained as 11 into 10 raised power minus 8 ohm into meter.

01:57So, for solution is R is equal to rho into L upon area.

02:14So, after rearranging this equation, L will be equal to R into A divided by rho is area

02:32is equal to pi R square.

02:34So, length will be equal to R into pi R square divided by rho.

02:47So, length will be equal to A, resistance is 40 ohm and the value of pi is 3.14 into

03:00R square means 0.05 into 10 raised to the power of minus 3 whole square divided by rho which

03:13is obtained as 11 into 10 raised to the power of minus 8 ohm into meter.

03:19So, length will be obtained as 40 into 3.14, it will be obtained as 125.6 into the square

03:34of 0.05 will be equal to 0.0025 into the square of 10 raised to the power minus 3 is 10 raised

03:47to the power minus 6 divided by 11 into 10 raised to the power minus 8.

03:53So, length will be obtained as 125.6 into 0.0025.

04:07It will be obtained as 0.314 into 10 raised to the power minus 6 divided by 11 into 10 raised

04:20to the power minus 8.

04:22So, 0.314 divided by 11.

04:26It will be obtained as 0.0285 into 10 raised to the power minus 10 raised to the power minus

04:3710 raised to the power minus 8.

04:37When the bases are same and deveyan, then we will subtract the power of denominator from

04:44the power of numerator.

04:46So when we will take minus 8 to the numerator, then it will be plus 8, so length will be

04:57obtained as 0.0285 into 10 raised power minus 6 plus 8, it will be plus 2 meters, 10 raised

05:10power plus 2 is equal to 100.

05:14So when we will multiply 100 with this value, then we will get the value of length as 2.85

05:23meters.

05:24So this is our final answer.

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