Question

If r1 is in series with parallel connected to r2 and r3, what happens to total current if r2 opens?

Answer 1

If r1 is in series with parallel connected to r2 and r3, the total current decreases if r2 opens.

Explanation:

Before opening of `r_2`

`R_(eq1)=r_1+(r_2r_3)/(r_2+r_3)`

`R_(eq1)=r_1+(r_3)/(1+r_3/r_2)` `" "color(green)((1))`

After opening of `r_2`:

hence `r_2=`infinity`" "color(green)((2))`

write down`" "color(green)((1))` after substitution of`" "color(green)((2))`

`R_(eq2)=r_1+r_3`[since`r_3/r_2=0` if `r_2`=infinity]

`R_(eq2)=r_1+r_3` `" "color(green)((3))`

from `" "color(green)((1))`&`color(green)((3))`

`R_(eq2)>R_(eq1)`

If resistance value is increased under constant application voltage and constant temperature ,then the rate of change of charge with respect to time decreases according to ohm's law.
`Iprop1/R` at constant voltage.

Therefore,the total current `color(blue)(decreases)` if r2 opens.