a resistor and a capacitor are connected in series to an ideal battery of constant terminal voltage. when the system reaches its steady state, what is the voltage across the resistor and the capacitor?
In a series circuit with a resistor and a capacitor connected to an ideal battery of constant terminal voltage, the voltage across the resistor and the capacitor will be different.
Voltage across the resistor:
In a steady state, the voltage across the resistor in a series circuit is equal to the voltage of the battery. This is because the resistor offers a constant amount of resistance to the flow of current, and according to Ohm’s Law (V = I * R), the voltage drop across a resistor is determined by the product of the current flowing through it and its resistance. Since the battery maintains a constant terminal voltage, the voltage across the resistor will also be constant and equal to the battery voltage.
Voltage across the capacitor:
In a steady state, the voltage across the capacitor in a series circuit will eventually become equal to the battery voltage but not immediately. Initially, when the circuit is first connected, the capacitor behaves like an open circuit and no current flows through it. Therefore, the voltage across the capacitor is zero. As time passes, the capacitor charges up and the voltage across it gradually increases. Eventually, when the charging process is complete and the system reaches its steady state, the voltage across the capacitor will be equal to the voltage of the battery.
It’s worth noting that the time it takes for the capacitor to charge up and reach its steady-state voltage depends on the capacitance of the capacitor and the resistance in the circuit. A higher capacitance or a larger resistance value will result in a longer charging time.