Suppose that Marcy was using a capacitor and two different value resistors, whic

Question

Suppose that Marcy was using a capacitor and two different value resistors, which of the following combinations in an RC circuit would give the greatest time constant when Marcy does this?
Select the correct answer.

a) the capacitor in series with the higher value resistor
b) the capacitor in series with both resistors in series with each other
c)the capacitor in series with the lower value resistor
d)the capacitor in series with both resistors in parallel with each other
PLease explain or show why you chose it, thanks!

Explanation / Answer

b) the capacitor in series with both resistors in series to each other. The time constant equals resistance multiplied by capacitance. So the larger your total R value, the larger your time constant (time constant=RC). When two resistors are in parallel to each other you have to add the reciprocals of their respective resistances and then take the reciprocal of the sum to get the combined resistance of both resistors, in other words, for parallel resistors Rtotal= (1/r1 + 1/r2)^-1. For two resistors in series, you simply add their respective resistances to get the combined resistance, in other words, Rtotal=r1 + r2. Take for example any case, for our purpose lets say r1=4 ohms and r2= 6 ohms. If the resistors were parallel then Rtotal= (1/4 + 1/6)^-1= (3/12 + 2/12)^-1= 12/5 =2.4 ohms. Whereas if the resistors were in series Rtotal= 4 +6 = 10 ohms. So if the resistors were in series to each other they would yield a greater total resistance, and when multiplied by C, would give you a larger time constant.

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