Using a resistor and two different value capacitors, which of the following comb

Question

Using a resistor and two different value capacitors, which of the following combinations in an RC circuit would give the greatest time constant?

a).the resistor in series with the larger value capacitor
b) .the resistor in series with both capacitors in series with each other
c)the resistor in series with the lower value capacitor d)the resistor in series with both capacitors in parallel with each other
a).the resistor in series with the larger value capacitor
b) .the resistor in series with both capacitors in series with each other
c)the resistor in series with the lower value capacitor d)the resistor in series with both capacitors in parallel with each other

Explanation / Answer

d) the resistor in series with both capacitors in parallel with each other. Time constant=RC. For capacitors in parallel to each other Ctotal= c1 + c2 and for capacitors in series with each other Ctotal= (1/c1 +1/c2)^-1. Its interesting to note that these equations are the exact opposite for that of resistors. For any set of values c1 and c2, the equation for parallel capacitors yields a larger total capacitance. So the largest time time constant would occur when the resistor is in series with both capacitors in parallel to each other.

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