The values of resistance r_1=33.3 ohm and r_2 = 41.7 ohm
The total resistance in series is the sum of the value of the resistances. Applying Ohm's law,
[tex] V=I(r_{1} +r_{2} [/tex] .....(1)
When the resistor r_1 is connected, the current increases by 0.2 A
Apply Ohm's law for the resistance r_1.
[tex] V=(I+0.2)r_{1} [/tex] ......(2)
When the resistor r_2 is connected, the current increases by 0.13 A.
Apply Ohm's law for the resistance r_2.
[tex] V=(I+0.13)r_{2} [/tex] ......(3)
From equations (1) and (2)
[tex] I(r_{1} +r_{2} )=(I+0.2)r_{1}
[/tex]
[tex] \frac{r_1+r_2}{r_1} =\frac{I+0.2}{I} \\ 1+\frac{0.2}{I} =1+\frac{r_2}{r_1} \\ \frac{r_2}{r_1} =\frac{0.2}{I} ......(4) [/tex]
Similarly from equations (1) and (3), it can be seen that
[tex] \frac{r_1+r_2}{r_2} =\frac{I+0.13}{I} \\ \frac{r_1}{r_2} =\frac{0.13}{I} ..... (5) [/tex]
From equations (4) and (5),
I=0.16 A
Substituting in equations (2) and (3)
[tex] r_1 =33.3 Ohm\\ r_2 =41.7 Ohm [/tex]
