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ss7ja [257]
3 years ago
7

The heat generated by a stove element varies directly as the square of the voltage and inversely as the resistance. If the volta

ge increases by a factor of 10​, what needs to be done to quadruple the amount of heat​ generated?
Physics
1 answer:
madam [21]3 years ago
3 0

Answer:

The resistance needs to be increased by a factor of 25 to quadruple the amount of heat generated

Explanation:

Let H be the heat generated by the stove element, V its voltage and R its resistance.

So, H ∝ V²/R

H = kV²/R

HR/V² = k

H₁R₁/V₁² = H₂R₂/V₂²

If H₂ = 4H₁ and V₂ = 10V₁

H₁R₁/V₁² = 4H₁R₂/(10V₁)²

H₁R₁/V₁² = 4H₁R₂/100V₁²

R₁ = R₂/25

R₂ = 25R₁

The resistance needs to be increased by a factor of 25 to quadruple the amount of heat generated.

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<h2>Answer:</h2>

143μH

<h2>Explanation:</h2>

The inductance (L) of a coil wire (e.g solenoid) is given by;

L = μ₀N²A / l                 --------------(i)

Where;

l = the length of the solenoid

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N = 183 turns

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<em>But;</em>

A = π d² / 4                     [Take π = 3.142 and substitute d = 0.00949m]

A = 3.142 x 0.00949² / 4

A = 7.1 x 10⁻⁵m²

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L = 4(3.142) x 10⁻⁷ x 183² x 7.1 x 10⁻⁵ / 0.0209

L = 143 x 10⁻⁶ H

L = 143 μH

Therefore the inductance in microhenrys of the Tarik's solenoid is 143

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