Question

The heat produced in a wire carrying an electric current
depends on the current, the resistance and the time.
Assuming that the dependence is of the product of powers
type, guess an equation between these quantities using
dimensional analysis. The dimensional formula of
resistance is ML^2T^-3and heat is a form of energy.​

Answer 1

Answer:

The heat produced in a wire carrying an electric current depends on the current, the resistance and the time. Assuming that the dependuance is of the product of powers type, guress an eqn. ... Since heat is a form of energy, its dimensioN/Al formula is ML3T-2.

Explanation:

Let the heat produced be H, the current through the wire be I, the resistnce be R and the time be t. Since heat is a form of energy, its dimensioN/Al formula is `ML^3T^-2`.

Let us assume that the required equation is

`h=kI^aR^bt^c`,

whre k is a dimensionless constant.

Writing dimension of both sides,

`ML^2T^_2=I^a(ML^2I^-2T^-3)^bT^c`

` =M^bL^(2b)T^(-3b+c)I^(a-2b)`

Equating the exponents,

`b=1`

`2b=2`

` -3b+c=0`

` a-2b=0` Soving these, we get `a=2, b1 and c=1`.

` Thus, the required equation is `H=kl^2 Rt.`

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