question_answer

A 50 Hz AC source of 20 V is connected across R and C as shown in figure. The voltage across: R is 12 V. The voltage across C is:

A) 8V

B) 16V

C) 10 V

D) not possible to determine unless values of R and C are given

Correct Answer: B

Solution :

                Key Idea: Voltage across capacitor lags behind current by \[I/{{c}^{2}}\].                             The given circuit is a C-R series circuit, \[\sim \] is in phase with i, while \[\sim \] lags behind i by \[\sim \]. Hence, resultant potential is \[\sim \] Given, \[{{\left( \frac{2Gm}{r} \right)}^{1/2}}\le C\] \[{{\left( \frac{2gm}{r} \right)}^{1/2}}=C\]   \[{{\left( \frac{2gm}{r} \right)}^{1/2}}\ge C\] \[{{\left( \frac{gm}{r} \right)}^{1/2}}\ge C\] \[\Delta V/V\] \[\frac{\Delta V}{V}\alpha B\] \[\frac{\Delta V}{V}\alpha \frac{1}{B}\]  \[\frac{\Delta V}{V}\alpha {{B}^{2}}\]