A battery, with potential V across it, is connected to a combination of two identical re- sistors and then has current i through it. What are the potential difference across and the current through either resistor if the resistors are (a) in series and (b) in parallel

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Explanation:

For a resistor connected in parallel, the potential difference across the resistors are the same. This means that the potential difference across the two identical resistors will be the same.

However, when the resistors are connected in series, the potential difference across resistors will be an addition of the voltage of each resistor. This means that the sum of the voltages of the two identical resistors will give the potential difference across the resistor.

It should be noted that the unit for potential difference is voltage.

To calculate the current running through a resistor, Ohm's law is followed.

Ohm's law states that the current flowing through a linear circuit is directly proportional to the potential difference across the circuit. Hence, the higher the potential difference, the higher the current passing through the circuit.

Thus, the formula for Ohm's law is V = IR

Where I is the current, V is the voltage and R is the resistance

In series, since we looking for I, the formula will be I = V/R

where V will be provided as the voltage the circuit is connected to, the resistance (R) will be the addition of the two identical resistance (R₁ + R₂)

In parallel, the formula here will also be I =V/R, however, the formula for resistance here will be a summation of the inverse of the two individual resistance as in (1/R₁ + 1/R₂)

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