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A Bimetallic strip is formed out of two identical strips one of copper $(α_{c})$ and the other brass $(α_{b})$ . On heating, the temperature of the strip increases by $Δ T$ and the strip bends to form an arc of radius R. Then R is

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Proportional to $Δ T$

Inversely proportional to $Δ T$

Proportional to $|α_{b} - α_{c}|$

inversely proportional to $|α_{b} - α_{c}|$

answer is B, D.

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Detailed Solution

$l_{b} = l_{0} (1 + α_{_{b}} Δ T) = (R + d) θ$

$l_{c} = l_{0} (1 + α_{_{c}} Δ T) = R θ$

$(1 + \frac{d}{R}) = (\frac{1 + α_{b} Δ T}{1 + α_{c} Δ T})$

$R = \frac{d}{(α_{b} - α_{c}) Δ T}$

$∴ R α \frac{1}{Δ T}$

$∴ R α \frac{1}{(α_{b} - α_{c})}$

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