Find the potential difference between the plates of the capactior C in the circuit shown in fig.5.236

Explanation

`X` to `X` path `XACX` , loop 1
`V_X-(i-i_(1))xx30-1xxi_(1)xx20=V_(X)`
`-30i + 50i_(1) = 1`..(i)
`X` to `X` path `XCBX`, 2
`v_(x)-i_(1)xx20-ixx10+4=V_(X)`
`10i + 20i_(1) = -4`..(ii)
Solving (i) and (ii)
`i = -1/5A`
`A` to `B` path `ACB`
`V_(A)-1-ixx10=V_B`
`V_(A)-V_(B)=1+10i = 1+10(-1//5)=1-2 = -1V`
p.d. across capacitor = `1V` point `B` is at higher potential.