Asked Dec 19, 2019

A particular wire has a resistivity of 3.0 x 10-8 Ω ⋅ m and a
cross - sectional area of 4.0 x 10-6 m2. A length of this wire is to
be used as a resistor that will develop 48 W of power when connected
across a 20. - V battery. What length of wire is required?


Expert Answer

Step 1

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Given info: The resistivity of a wire is 3.0 x 10-8N.m and the crss sectional area is 4.0 x 10-6 m². The power which is received if wire is used as a resistor is 48 W and the voltage source is 20 V. Formula to calculate the resistance of the wire is, pl R Here, Ris the resistance of the wire. A is the area of the wire. l is the length of the wire. pis the resistivity. Rearrange the above equation for l, l = RA (1)

Step 2

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Formula to calculate the power dissipated by the resistor is, AV² Here, Pis the power. AV is the voltage drop across the resistor. Substitute 48 W for P and 20 V for AV in above equation. (20 V)? 48 W (20 V)? R = 48 W = 8.33 N


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