Question

Obtain the expression for the heat developed in a resistor by the passage of electric current through it. 220 J of heat is produced each second in a 8Ω resistor. Find the potential difference across the resistor.

Answer 1

Explanation:

so the resistor produces 220j in 1second

so potential difference across the resistor in 1 second equals.......

resistance=8ohm

t=1second,r=8ohm,U=220J

U=V^2/R×t

220=V^2/8×1

220×8=V^2

V^2=1760

V=sqrt 1760=41.95 volt

Answer 2

☑️ Heat produced in a conductor or a resistor due to the passage of electric current through it depends on the resistance of the conductor, strength of current and time of flow of current. If we denote the heat produced in a conductor or a resistor due to the passage of electric current through it by H, resistance of the conductor by R, strength of current by I and time of flow of current by t, then, according to James Presscot Joule's laws of heating effect of electric current,

✳️ H ∝ I² (when R and t are constant)

✳️ H ∝ R (when I and t are constant)

✳️ H ∝ t (when I and R are constant)

Combining these above three laws (by the rule of JOINT VARIATION), we get :

H ∝ I²Rt (when I,R,t all vary)

So, H ∝ I²Rt

or, H = (1/J) × I²Rt [where, 1/J is the proportionality constant and "J" is known as mechanical equivalent of heat]

or, H = (I²Rt)/J

In S.I. system, J=1, and hence, the expression can be written as : H = I²Rt joule

So, the expression for the heat developed in a resistor by the passage of electric current through it is H = (I²Rt)/J (where, symbols have their usual meanings which are discussed at the beginning)

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☑️ Next question's solution is given in the picture which is attached with this answer !