Question

In a parallel resistor circuit connected to a battery, the voltage across each resistor is the same as____ _____ _____, and the sum of the currents through each resistor must:

a) The battery voltage, add up to zero
b) The sum of their resistances, be equal to the battery voltage
c) The current through the battery, be equal to the sum of the resistances
d) The sum of their resistances, be zero

Answer 1

In a parallel resistor circuit, the voltage across each resistor is equal to the battery voltage, while the sum of the currents through each resistor equals the total current from the battery.

Step-by-step explanation:

In a parallel resistor circuit connected to a battery, the voltage across each resistor is the same as the battery voltage. This means for a parallel configuration that Vbattery = V1 = V2 = V3.... Additionally, the sum of the currents through each resistor must be equal to the total current flowing from the battery. Therefore, the current through each resistor in a parallel circuit might differ, depending on the resistance of each resistor, but the sum of these currents equals the current from the battery.

So, the correct answer to the question is: a) The battery voltage, add up to zero. This addresses the concept that in parallel circuits, the voltage across each component is the same as the battery voltage, and the total current flowing into the node before the parallel resistors is equal to the sum of the currents flowing through each parallel resistor.

Contrastingly, resistors connected in series will have the same current flowing through them, and the total voltage across them sums up to the battery voltage. Each series resistor will have a different voltage drop across it, which depends on its resistance.