Final answer:
To find the current through the resistor 6 seconds after closing the switch, one must calculate the voltage across the capacitor using V_c = ε(1 - e^{-t/RC}) and then apply Ohm's law with the calculated voltage and resistor value.
Step-by-step explanation:
An RC circuit generally consists of a resistor and a capacitor which are connected either in series or parallel with a battery. In the question provided, a circuit consists of a battery, a 100 kΩ resistor, a 20.0 μF capacitor, and a switch. To calculate the current through the resistor 6.00 seconds after the switch is closed, we use the charging formula of a capacitor V_c = ε(1 - e^{-t/RC}), where V_c is the voltage across the capacitor, ε is the EMF of the battery, R is the resistance, C is the capacitance, t is the time, and e is Euler's number (approximately 2.71828).
First, we find the voltage across the capacitor at time t = 6.00 seconds, and then use Ohm's law to find the current through the resistor.
The RC time constant (τ = RC) for the circuit is (100 × 10^3 Ω)(20.0 × 10^{-6} F) = 2 seconds. Plugging in the values into the charging formula, we get:
V_c = 15.1 V × (1 - e^{-6/2})
= 15.1 V × (1 - e^{-3})
= 15.1 V × (1 - e^{-1.5})
After calculating V_c, the current I through the resistor can be determined using Ohm's law I = V_c / R.