Final answer:
The potential across a capacitor being charged through a resistor by a battery is calculated using the formula V(t) = V0(1 - e^-t/RC). The time constant (τ) is CR, which in this case is 10 seconds. The voltage on the capacitor can then be calculated at different times using this time constant.
Step-by-step explanation:
To determine the potential across a capacitor at various times when being charged through a resistor by a battery, we use the formula:
V(t) = V0(1 - e-t/RC) (charging),
where V(t) is the potential across the capacitor at time t, V0 is the potential of the battery, R is the resistance, C is the capacitance, and e is the base of the natural logarithm.
The time constant (τ) is given by the product of the resistance (R) and the capacitance (C),
τ = RC,
For our given values, τ = (10 x 106 Ω)(1.0 x 10-6 F) = 10 seconds. Now we can calculate the voltage on the capacitor at different times.
At t = 1.0s, we have
V(1.0) = 6.0V(1 - e-1.0/10)
At t = 5.0s, the equation becomes
V(5.0) = 6.0V(1 - e-5.0/10)
Finally, at t = 20s, the equation is
V(20) = 6.0V(1 - e-20/10)