Series and parallel circuits

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I = DeltaV/R (1)

I is the current through the resistor (A)

Delta V is the potential different through the resistor (V)

R is the resistance of the resistor ()

By modifying equation 1, the resistance of a resistor can be determined if the voltage and the current is known which is represented in this equation:

R = Delta V/I (2)

Hence, by this equation obtained, the resistance of a resistor can be seen as a slope of the potential energy (Delta V) as a function of the current (I).

As mentioned before, there are two types of way resistors can be placed in a circuit. They can be placed in series or in parallel.

Resistors in Series

Resistors placed in series are aligned in a way where the current through one resistor goes directly though the next resistor means that the current remains constant throughout the circuit. With a constant current and resistors with different resistance, the potential difference across the power source is equal to the sum of the potential differences across each resistor. Additionally, the equivalent resistance is equal to the sum of all the individual resistance as described in this equation:

Req = R1 + R2 + … + RN (3)

Resistors in Parallel

Resistors in parallel are connected together at both ends. Hence, the potential energy across each resistor is constant. The current through the power source is equal to the sum of the currents through each branch of the circuit as described in this equation:

I = I1 + I2 + … + IN (4)

Furthermore, the resistors in parallel can be combined as an equivalent resistance which is equal to the sum of the reciprocals of each individual resistance as described in this equation: (5)