Question

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

Answer 1

Answer:

2 unequal resistances, R1 and R2

Ie connected across two identical batteries of

=emfE

An internal resistance

R (figure). Canthethermal not equal to rgiesdev

R1 and R2

Answer 2

Explanation:

It is given that time is t.

The current passing via the resistance R1 and R2 be i1 and i2, respectively. Kirchoff’s voltage law lies at the heart of the analysis of circuit.  

When Kirchoff’s Voltage Law is applied to circuit-1, we get:

$\varepsilon-i 1 r-i 1 R 1=0 \Rightarrow 11=\varepsilon r+R 1$

Similarly, in the other circuit, the current,

$12=\varepsilon r+R 2$

Through the resistances, the thermal energies are given by

$\text { IIZRIt }=122 \mathrm{R} 2 \mathrm{t} \varepsilon \mathrm{r}+\mathrm{R} 12 \mathrm{R} 1 \mathrm{t}=\mathrm{R} 2-\mathrm{R} 1 \mathrm{r} 2 \times \mathrm{R} 2-\mathrm{R} 1 \mathrm{R} 1 \mathrm{R} 2=\mathrm{R} 2-\mathrm{R} 1 \mathrm{r} 2=\mathrm{R} 1 \mathrm{R} 2 \Rightarrow \mathrm{r}=\mathrm{R} 1 \mathrm{R} 2$