Choose the graph of Brightness vs Time below that most accurately describes the

Question

Choose the graph of Brightness vs Time below that most accurately describes the time behavior of the brightness of the light bulb in the center branch of the circuit shown. Note that the lower-right branch (with a capacitor) has a resistor of value 2R, while the lower-left branch (with an inductor) has a resistor of value R. As always, defend your choice!  

loose the graphi Brighthess vstlme below e br gritness vs time below that Question: Choose the graph of Brightness vs Time below that hoose the graph of Brightness vs Time below that most accurately describes the time behavior of the brightness of the light bulb in the center branch of the circuit the lowerright branch (with a has a resistor of value 2R, while the lower-left branch (with an in has a resistor of value R YOU MUSTEXPLAIN CHOICE show transcribed image text comments /study/tbs

Explanation / Answer

initially capacitor will be short circuit and inductor will be open circuit.

so the only path for current is through C,C and 2*R.

as capacitor is short circuit, initial current=V/(2*R)

as power dissipated through middle resistance is directly proportional to square of the current

at steady state, capacitor will be open circuit and inductor will be short circuit

only path avaiable is through L,L and R,

current =V/R

so the brightness will start from a lower value and end at a higher value

this requirement matches with only graph c

hence graph c is the correct option.

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