Kirchoff's Rules and Resistors in Series/Parallel | MCAT Physics Prep

Need help preparing for the MCAT physics section? MedSchoolCoach expert, Ken Tao, will teach you what you need to know about Kirchoff's rules and resistors in series/parallel which is an important circuits component. Watch this video to learn how to do well on the physics section of the MCAT exam!

Kirchhoff’s two rules allow us to calculate the resistance, current, and voltage in a circuit. Rule one is the junction rule, which states that the total current entering a junction has to equal the total current exiting that junction. It can be related to the conservation of charge: however much charge enters a junction has to be the same amount of charge that exits the junction.

Rule two is the loop rule, which states that the sum of the voltages around any closed loop in a circuit is zero. In a typical circuit, we know that a battery is supplying some voltage (Vbat) to induce a current. As the current passes through each resistor in a circuit, there will be a voltage drop -V1, -V2, and so on until the voltage passes through the last resistor.

Resistors in Series

Circuit elements can be connected to a circuit in two different patterns: in series or in parallel. Connecting circuit elements in series is to connect them in such a way that there's one common path for current flow – imagine connecting them in a straight line. What does it mean for resistors to be connected in series? If two resistors are connected in series, and we know that 2 A of current passes through the first resistor, then we also know that 2 A of current passes through the second resistor. Next, when resistors are connected in series, how do we use Kirchhoff’s loop rule to find the voltage drop at each element in the circuit? We know that as current passes through each of these resistors, there's going to be a voltage drop across each resistor, and Kirchhoff’s loop rule tells us the total voltage drop (V1 + V2 + … + Vn) must equal the voltage of the battery (Vbat). Lastly, how can we calculate the total effective resistance when you have three resistors connected in series? Resistance for resistors added in series is additive, so the total resistance is equal to their sum.

Resistors in Parallel

When resistors are connected in parallel, there are multiple separate paths for current to flow through. If current is flowing through the circuit but reaches a junction in the circuit, the amount of current that enters the junction has to be the same amount of current that exits the junction. Current will split up between the two paths, but the total amount of current will be equal to the sums of the individual currents, based on the junction rule. Next, the loop rule states the total voltage around any closed loop is equal to zero. In a circuit with parallel branches, there are multiple closed loops that pass through one of the branches, and across any of the closed paths you pass through only one resistor. The total voltage drop must be the same no matter what branch you take (equal to Vbat), and so the resistors on each branch in the circuit must experience the same voltage drop. Therefore, when you're dealing with resistors in parallel, the voltage drop across each element can be understood by considering the element in terms of a closed loop. Lastly, how does resistance change when resistors are in parallel? Placing resistors in parallel can be thought of as opening up more paths for current to pass through, which actually decreases overall resistance. The equation describing this is shown below.

Capacitors in Series and Parallel

Capacitors are circuit elements that store electrical energy. We will briefly contrast how to calculate total capacitance for capacitors in series and parallel with calculating total resistance. If you have capacitors in series, total capacitance is calculated similarly to resistors in parallel. Total capacitance decreases, as shown by the equation below.

The capacitance of capacitors in parallel is additive. This is similar to calculating the resistance of resistors in series.

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