When an ac source of e.m.f. \[e={{E}_{0}}\]\[\sin (100\,t)\] is connected across a circuit, the phase difference between the e.m.f. e and the current i in the circuit is observed to be \[\pi /4\], as shown in the diagram. If the circuit consists possibly only of RC or LC in series, find the relationship between the two elements [IIT-JEE (Screening) 2003]

• A.            \[R=1k\Omega ,\,C=10\mu F\]                                        
• B.            \[R=1k\Omega ,\,C=1\mu F\]
• C.            \[R=1k\Omega ,\,L=10H\]      
• D.            \[R=1k\Omega ,\,L=1H\]