Final answer:
The behavior of the current through R1 and the voltage across it depends on the circuit configuration and external influences. In a simple series circuit with an increasing R1 resistance, the current decreases, but in an RC charging circuit, the current and voltage would initially increase then decrease. In parallel circuits, altering one resistor's resistance does not change the voltage or current through the other resistor.
Step-by-step explanation:
The current through R1 and the voltage across the resistor can increase, decrease, or have variable behavior depending on the specific characteristics of the circuit and the context in which the question is asked. For instance, in a simple series circuit with a constant voltage supply, if the resistance R1 increases, according to Ohm's law (V = IR), the current through the resistor would decrease.
If two resistors are in parallel and one increases its resistance, the total parallel resistance increases, which could lead to a decrease in the overall current through the branch containing R1 if it is the resistor that increased its resistance.
In the context of a charging or discharging capacitor in an RC circuit, the current through the resistor and the voltage across it will indeed initially increase as the capacitor charges and then decrease as it reaches its full charge (option c). Once the capacitor is fully charged, the current through the resistor would be zero because the capacitor acts like an open circuit, preventing current flow.
When you double the voltage across an ohmic resistor, the current will also double (option a), following Ohm's law.
If two resistors are connected in parallel and one increases its resistance, the voltage across the other resistor remains the same due to the parallel connection maintaining the voltage constant, but the current through the resistor with unchanged resistance also remains the same because the voltage across it has not changed (option a).