If in the circuit shown below, the internal resistance of the battery is `1.5 Omega` and `V_(P)` and `V_(Q)` are the potential at `P` and `Q` respectively, what is the potential difference between the point `P` and `Q`?

Options

A. Zero
B. `4 V(V_(P) gt V_(Q))`
C. `4 V (V_(Q) gt V_(P))`
D. `2.5 V (V_(Q) gt V_(P))`

Answer

D

Explanation

Resistances (3+2) and (2+3) are in parallel.
`therefore` Their effective resistance `=(5)/(2) Omega = 2.5 Omega`
`therefore I=(20)/(2.5+1.5)=5 A`
`therefore` Current will be equally divided in APB and AQB .
`therefore V_(A)- V_(P)=(i)/(2)xx3 =(5)/(2)xx3=7.5V`
and `V_(A)-V_(Q)=(5)/(2)xx2= 5 V`
`therefore V_(A)-V_(Q)-V_(A)+V_(P)=(5-7.5)`
`therefore V_(P)-V_(Q)= -(2.5 V) or V_(Q)- V_(P)=2.5 V`