Question

If a resistor is connected in parallel to a resistor in an existing circuit, while voltage remains constant, which of the following is true of the circuit? a) resistance, current, and power increase b) resistance, current, and power decrease c) resistance increases and current and power decrease d) resistance decreases and current and power increase

Answer 1

Increasing the resistance of one resistor in a parallel circuit decreases the overall current, but the voltage across the remaining resistors stays constant. Therefore, the current through the unaffected resistor decreases, while the voltage across it remains unchanged.

Step-by-step explanation:

When two resistors are connected in parallel to a voltage source and you increase the resistance of one resistor, the overall effect is the decrease of the total resistance of the circuit. Since the voltage across resistors in parallel is constant, Ohm's Law tells us that an increase in one resistor's resistance doesn't change the voltage across the other resistor. However, the current through the other resistor may change due to the change in the overall current in the circuit. Specifically, if resistance is increased in one branch of a parallel circuit, the total resistance will increase, leading to a decrease in total current. Since the voltage across the resistors in parallel remains the same, the current through the unchanged resistor will now share a reduced total current, and hence, it will decrease, not increase. Therefore, the correct answer is that the current through the unaffected resistor decreases and the voltage across it remains the same.

Answer 2

OPTION D.

When a resistor is added in parallel to an existing circuit with constant voltage, the overall resistance decreases while both current and power increase.

Step-by-step explanation:

If a resistor is connected in parallel to a resistor in an existing circuit, while the voltage remains constant, the following happens in the circuit: the overall resistance decreases and, as a result, the current and power increase. This is due to the nature of parallel circuits where adding more pathways for the current reduces the total resistance and allows more current to flow through the circuit as per Ohm's law (V=IR).

Regarding the specific options from the original question: d) resistance decreases and current and power increase is the correct one. When resistors are added in parallel, each additional resistor provides a new path for current to flow, which reduces the total resistance according to the parallel resistor formula 1/Rtotal = 1/R1 + 1/R2 + ... 1/Rn. Because voltage is constant, the current through the circuit increases with the decrease in resistance, which in turn increases the power dissipated in the circuit given by P=VI, where P is power, V is voltage, and I is current.