In part (a) of the figure below , the switch is closed on point a . After closin

Question

In part (a) of the figure below , the switch is closed on point a. After closing the switch, there is a current i through resistance R. Part (b) of the figure below gives that current, as a function of time, for four sets of values of R and capacitance C: (1) R0 and C0, (2) 2R0 and C0, (3) R0 and 2C0, (4) 2R0 and 2C0. Which set goes with which curve?

Set (1) goes with curve ? a, b, c, or d? 1??
Set (2) goes with curve ? a, b, c, or d? 2??          
Set (3) goes with curve ? a, b, c, or d?   3a, b, c, or d?
Set (4) goes with curve ? a, b, c, or d?

In part (a) of the figure below , the switch is closed on point a. After closing the switch, there is a current i through resistance R. Part (b) of the figure below gives that current, as a function of time, for four sets of values of R and capacitance C: (1) R0 and C0, (2) 2R0 and C0, (3) R0 and 2C0, (4) 2R0 and 2C0. Which set goes with which curve?

Explanation / Answer

maximum current in the circuit = e.m.f.? /resistance. So maximum current will be double in case resistance isR0 than when it is2R0. Hence curves a and d are associated with (1) and (3), whereasband c with (2) and (4). Further decay of current is directly propotional toexp(-1/(capacitance x resistance)). When the product of capacitanceand resistance is less the curve falls of more rapidly. Hence cuve d is associated with (1) and a with (3). similarlycurve b is associated with (2) and c with (4).

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