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

Answer:

$0.01\ \text{A}$

$0.0015\ \text{C}$

$0.0608\ \text{s}$

Explanation:

$V_0$ = Voltage = 1.5 V

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

$R$ = Resistance = $150\ \Omega$

Current is given by

$I=\dfrac{V_0}{R}\\\Rightarrow I=\dfrac{1.5}{150}\\\Rightarrow I=0.01\ \text{A}$

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

Charge is given by

$Q=CV\\\Rightarrow Q=1000\times 10^{-6}\times 1.5\\\Rightarrow Q=0.0015\ \text{C}$

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

Voltage is given by

$V=V_0e^{-\dfrac{t}{RC}}\\\Rightarrow t=-RC\ln\dfrac{V}{V_0}\\\Rightarrow t=-150\times 1000\times 10^{-6}\times\ln\dfrac{1}{1.5}\\\Rightarrow t=0.0608\ \text{s}$

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