The equivalent resistance of a group of resistances is $R$. If another resistance is connected in parallel to the group , its new equivalent becomes $R_1$ and if it is connected in series to the group , its new equivalent becomes $R_2$ we have :
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The equivalent resistance of the group of resistances is $R.$
case $1:$
a resistance $r(\text { say })$ is connected in parallel to the group, its new equivalent resistance $R1$ is
$R_{1}=\frac{R r}{R+r}$
hence, $R_{1} < R$
case $2:$
a resistance $r$ is connected in series to the group, its new equivalent resistance $\mathrm{R} 2$ is
$R_{2}=R+r$
hence, $R_{2}>R$
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