Find the potential difference between $a$ and $b$, as shown in the below circuit.

Consider the following two circuits

$\left[A\right] :$ $20$ bulbs are connected in series to a power supply line

$\left[B\right] :$ $20$ bulbs identical to $\left[A\right]$ are connected in a parallel circuit to an identical power supply line

Identify which of the following is not true

The resistance in following circuit are $R_1=R_2=R_3=6.0 \mathrm{\Omega }.$ The emf of the battery is $12$ volts. When switch $S$ is closed, the potential across resistance $R_1$ is changed by an amount.