Q. 24.0( 1 Vote )

Two unequal resistances R1 and R2 are connected across two identical batteries of emf ϵ and internal resistance r. Can the thermal energies developed in R1 and R2 be equal in a given time. If yes, what will be the condition?



Answer :

Given as emfs of the circuits with internal resistances r


Let the currents passing through the


resistance R1 and R2 be i1 and i2 , respectively for time t.


According to Kirchhoff’s Voltage Law, sum of


all voltages around any closed loop in a


circuit must equal zero.


Capture.PNG


ie,


Looking into the circuit 1-we get-



(1)


Similarly, the current in the other circuit,


(2)


The heat lost through a resistor r is given by


(3)


Now the total thermal energies through the resistances from Joule’s heating effect are given


by -


=


From(1), (2) and (3)


( = (


( = (


( = (






Hence, the condition when the thermal energies developed in


R1and R2 be equal in a given time is when the internal resistance r–



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