As more identical resistors R are added to the parallel circuit shown here, the

Question

As more identical resistors R are added to the parallel circuit shown here, the total resistance between points P and QB A) increases. B) remains the same. C) decreases The capacitive network shown in the figure is assembled with initially uncharged capacitors. A potential difference, V_ab = + 100V, is applied across the network. The switch S in the network is initially open but is then closed. Assume that all the capacitances shown are accurate to two significant figures. What is the equivalent capacitance between ab. with the switch S open? A. 25mu F B. 14 mu F C. 19 mu F D. 36 mu F

Explanation / Answer

1. We have 1/Req=1/R+1/R+1/R+1/R +.......

=n/R

Therefore, Req= R/n

As n increases Req decreases.

2. When the switch S is open,

the upper 2 capacitances of 9 and 15 microfarads are in parallel resulting in an equivalent capacitance of 24 microfarads.Also the lower 3 capacitances which are in parallel add up resulting equivalent capacitance of 24 microfarads.

Thus, we have in effect 2 capacitances of 24 and 16 microfarads in series to the left of the switch S and 2 capacitances of 6 and 24 microfarads to the right of the switch.

The equivalent capacitance of the 2 capacitances in series to the left of S=1/(1/24+1/16)=48/5=9.6 microfarads.

The equivalent capacitance of the 2 capacitances in series to the right of S=1/(1/6+1/24)=24/5=4.8 microfarads.

Therefore, the total equivalent capacitance C=9.6+4.8=14.4 microfarads.

Ans. B

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