It is not possible to change the voltage instantaneously across a resistor because resistors inherently oppose changes in voltage due to their resistance. When a voltage is applied across a resistor, the resistor restricts the flow of current according to Ohm’s law (V = IR), where V is voltage, I is current, and R is resistance. Any change in voltage across the resistor causes a corresponding change in current, and this change occurs over a period of time dictated by the resistor’s resistance and the circuit characteristics. Therefore, while voltage changes can occur across a resistor, they cannot happen instantaneously due to the resistor’s inherent opposition to sudden changes in current flow.

Voltage across a capacitor cannot change instantaneously because capacitors store electrical charge, and the rate of change of voltage across a capacitor is proportional to the current flowing into or out of the capacitor. When a voltage is applied or changed across a capacitor, the capacitor charges or discharges through the flow of current. The time it takes for the capacitor to charge or discharge, known as the time constant (τ = RC for a series RC circuit), determines how quickly the voltage across the capacitor can change. This charging or discharging process does not occur instantaneously and is governed by the capacitor’s capacitance and the resistance in the circuit.

Voltage changes across a resistor occur due to the flow of electrical current through the resistor. When current flows through a resistor, it experiences a voltage drop according to Ohm’s law. This voltage drop is proportional to the current flowing through the resistor and the resistance value of the resistor (V = IR). As current varies or as resistance values change in a circuit, the voltage across the resistor adjusts accordingly. Therefore, changes in voltage across a resistor are a direct result of the electrical current passing through it and the resistance offered by the resistor.

Inductor current cannot change instantaneously because an inductor opposes changes in current flow due to its inherent property of inductance. When current flows through an inductor, it generates a magnetic field. Any change in current through the inductor induces a voltage (known as back EMF) that opposes the change in current. This phenomenon is described by Faraday’s law of electromagnetic induction. As a result, the rate of change of current through an inductor is limited by the inductance value of the inductor and the circuit characteristics. Therefore, inductor current cannot change instantaneously and requires a finite amount of time to increase or decrease, depending on the applied voltage and the circuit conditions.