13 and 14 please 12. Two resistors connected in series have an equivalent resist

Question

13 and 14 please

12. Two resistors connected in series have an equivalent resistance of 690 . When they are connected in parallel their equivalent resistance is 150 . Find the resistance of each resstor. 13. An uncharged capacitor and a resistor are connected in series to a source of emf. If emf = 9.00 V, C = 20.0 F, and R = 100 find A) the time constant of the circuit, B) the maximum charge on the capacitor, and C) the charge on the capacitor at a time equal to one time constant after the battery is connected 14. A 10.0 F capacitor is charged by a 10.0 V battery through a resistance R. The capacitor reaches a potential difference of 4.00 V in a time interval of 3.00 s after arging begins. Find R.

Explanation / Answer

13)Given,

emf = 9 V ; C = 20 uF ; R = 100 Ohm

A)time constant of the RC circuit is given by:

tau = RC

tau = 100 x 20 x 10^-6 = 2 x 10^-3 s

Hence, t = 2 x 10^-3 s = 2 ms

b)Q = CV

Q = 20 x 10^-6 x 9 = 180 x 10^-6 C

Hence, Q = 180 x 10^-6 C = 180 uC

C)Q' = Q (1 - e^-t/RC)

Q' = 180 x 10^-6 (1 - e^-2 x 10-3/2 x 10^-3) = 180 x 10^-6 (1 - 0.368) = 113.76 x 10^-6 C

Hence, Q' = 113.76 x 10^-6 C = 113.78 uC

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