Question

A 1.5 V battery is connected to a 1,000 μF capacitor in series with a 150 Ω resistor. a. What is the maximum current that flows through the resistor during charging? b. What is the maximum charge on the capacitor? c. How long does the capacitor take to reach a potential of 1.0V?

Answer 1

`0.01\ \text{A}`

`0.0015\ \text{C}`

`0.0608\ \text{s}`

Step-by-step explanation:

`V_0` = Voltage = 1.5 V

`C` = Capacitance =
`1000\ \mu\text{F}`

`R` = Resistance =
`150\ \Omega`

Current is given by

`I=(V_0)/(R)\\\Rightarrow I=(1.5)/(150)\\\Rightarrow I=0.01\ \text{A}`

Current flowing in the resistor is
`0.01\ \text{A}`.

Charge is given by

`Q=CV\\\Rightarrow Q=1000* 10^(-6)* 1.5\\\Rightarrow Q=0.0015\ \text{C}`

The charge on the capacitor is
`0.0015\ \text{C}`.

Voltage is given by

`V=V_0e^{-(t)/(RC)}\\\Rightarrow t=-RC\ln(V)/(V_0)\\\Rightarrow t=-150* 1000* 10^(-6)*\ln(1)/(1.5)\\\Rightarrow t=0.0608\ \text{s}`

Time taken to reach 1 V is
`0.0608\ \text{s}`.