Question

You want to replace the resistor in your

Answer 1

To make the boiler more efficient, we would replace the resistor with another double the length.

We know that the resistance of the resistor in the boiler is given by R = ρl/A where

• ρ = resistivity,
• l = length of resistor and,
• A = cross-sectional area of resistor.

Also, the power generated by the resistor is P = i²R where

• i = current and
• R = resistance.

If i is constant, we see that P ∝ R.

So, to increase the efficiency, the value of the resistance has to increase.

Also, since R = ρl/A and ρ and A are constant, we see that R ∝ l.

Since P ∝ R and R ∝ l ⇒ P ∝ l.

So, to increase the efficiency, we would double the length of the resistor.

So, to make the boiler more efficient, we would replace the resistor with another double the length.

Learn more about resistors here:

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