PHYSICS
PHYSICS
5th Edition
ISBN: 2818440038631
Author: GIAMBATTISTA
Publisher: MCG
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Chapter 18, Problem 103P

(a)

To determine

Find the resistance of the heater.

(a)

Expert Solution
Check Mark

Answer to Problem 103P

The resistance of the heater is 6.5 Ω.

Explanation of Solution

Write the equation for resistance from power.

R=V2P (I)

Here, P  is the power, V is the potential difference and R is the resistance.

Conclusion:

Substitute 120 V for V and 2200 W for P in equation I.

R=(120 V)22200 W=6.5 Ω

Therefore, the resistance of the heater is 6.5 Ω.

(b)

To determine

Find the current in the wire.

(b)

Expert Solution
Check Mark

Answer to Problem 103P

The current in the wire is 18 A.

Explanation of Solution

Write the equation for current from power.

I=PV (II)

Here, I is the current.

Conclusion:

Substitute 120 V for V and 2200 W for P in equation II.

I=2200 W120 V=18 A

Therefore, the current in the wire is 18 A.

(c)

To determine

Find the diameter of the wire.

(c)

Expert Solution
Check Mark

Answer to Problem 103P

The diameter of the wire is 0.86 mm.

Explanation of Solution

The wire has a circular cross section, then write the equation for area of this cross section.

A=14πd2 (III)

Here, A is the area of the wire.

Write the equation for resistance of the wire.

R=ρLA (IV)

Here, R is the resistance, ρ is the resistivity and L is the length of the wire.

Write the equation for resistivity.

ρ=ρ0(1+αΔT) (V)

Here, ρ is the resistivity, ρ0 is the initial resistivity, α is the temperature coefficient of resistivity and ΔT is the change in temperature.

Substitute equation III and V in equation IV.

R=ρ0(1+αΔT)L14πd2

Rewrite the above equation to get diameter of the wire,

d=4ρ0(1+αΔT)LπR (VI)

Conclusion:

Substitute 108×108 Ωm for ρ0, 0.00040 °C1 for α, 420 °C20 °C for ΔT, 3.0 m for L and 6.5 Ω for R in equation VI.

d=4(108×108 Ωm)(1+(0.00040 °C1)(420 °C20 °C))(3.0 m)π(6.5 Ω)=0.86 mm

Therefore, the diameter of the wire is 0.86 mm.

(d)

To determine

Find the current in the wire when it is turned on.

(d)

Expert Solution
Check Mark

Answer to Problem 103P

The current in the wire when it is turned on is 21 A.

Explanation of Solution

Write the equation for resistance.

R=R0(1+αΔT) (VII)

Here, R0 is the initial resistance.

Write the equation for current

I=VR0 (VIII)

Conclusion:

Substitute 0.00040 °C1 for α and 420 °C20 °C for ΔT in equation VII.

R=R0(1+(0.00040 °C1)(420 °C20 °C))R0=R1.16

Substitute the above value in equation VIII.

I=1.16VR=1.16VV2P=1.16PV

Substitute 120 V for V and 2200 W for P in above equaiton.

I=1.16(2200 W)120 V=21 A

Therefore, the current in the wire when it is turned on is 21 A.

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Chapter 18 Solutions

PHYSICS

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