A 100 F capacitor is connected in a series with a10 resistor and a 4.5V battery

Question

A 100 F capacitor is connected in a series with a10 resistor and a 4.5V battery that can be turned off and on.The capacitor is initially fully charged:
A) When will the voltage drop across the 10 resistor beequal to 1.5V after the switch is closed? B) If the battery is switched off after the capacitor is fullycharged and the capacitor then discharged through the circuit, howlong will it take for the voltage across the 10 resistor todrop to 1V ? A) If V = V(1-e^-t/RC)     (1/3) =(1-e^-t/RC)      I don't know how tomanipulate the formula to get t. B) V = V(1-e^-t/RC)      (1/4.5) = (1-e^-t/RC)   How to solve this for t. Please insert appropriate values into these formulas.Thanks Not a text problem A 100 F capacitor is connected in a series with a10 resistor and a 4.5V battery that can be turned off and on.The capacitor is initially fully charged:
A) When will the voltage drop across the 10 resistor beequal to 1.5V after the switch is closed? B) If the battery is switched off after the capacitor is fullycharged and the capacitor then discharged through the circuit, howlong will it take for the voltage across the 10 resistor todrop to 1V ? A) If V = V(1-e^-t/RC)     (1/3) =(1-e^-t/RC)      I don't know how tomanipulate the formula to get t. B) V = V(1-e^-t/RC)      (1/4.5) = (1-e^-t/RC)   How to solve this for t. Please insert appropriate values into these formulas.Thanks Not a text problem

Explanation / Answer

. 1.   I'll walk through the steps to solve for't'. . 2.   V1 = (V2)*{1 -exp[(-t)/()]}      ;   divide both sides by V2 3.   (V1)/(V2) =1-exp[(-t)/()]         ; subtract 1 from both sides 4.   (V1)/(V2) - 1 =-exp[(-t)/()]         ; multiply both sides by -1 5.   1 - (V1)/(V2) =exp[(-t)/()      ;   takethe natural log of both sides; note: ln[exp()] = 5.   ln[1 - (V1)/(V2)] = (-t)/()        ;  multiply both sides by 6.   ()*ln[1 - (V1)/(V2)] =(-t)      ;   multiply bothsides by -1 and rearrange 7.   t = (-)*ln[1 - (V1)/(V2)] .

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