Using the formulas for series and parallel circuits, fill in...

Using the formulas for series and parallel circuits, fill in the blanks in the tables shown opposite each circuit. In the blanks across from Battery under $V:$ Write the emf of the battery. I: Write the total current in the circuit. $R$ : Write the equivalent or total resistance of the entire circuit. In the blanks across from $R_{1}$ under $V:$ Write the voltage drop across $R_{1}$ I: Write the current flowing through $R_{1}$. $R:$ Write the resistance of $R_{1} .$ In the blanks across from $R_{2}, R_{3}, \ldots,$ fill in the appropriate numbers under $V, I,$ and $R$. (Begin by looking for key information given in the table and work from there.) $$ \begin{array}{cccc} & \boldsymbol{V} & \boldsymbol{I} & \boldsymbol{R} \\ \hline \text { Battery } & \mathrm{V} & \mathrm{A} & \Omega \\ R_{1} & 12.0 \mathrm{~V} & \mathrm{~A} & 2.00 \Omega \\ R_{2} & \mathrm{~V} & \mathrm{~A} & 4.00 \Omega \\ R_{3} & 24.0 \mathrm{~V} & \mathrm{~A} & 4.00 \Omega \\ R_{4} & \mathrm{~V} & \mathrm{~A} & 8.00 \Omega \end{array} $$

Using the formulas for series and parallel circuits, fill in the blanks in the tables shown opposite each circuit. In the blanks across from Battery under
$V:$ Write the emf of the battery.
I: Write the total current in the circuit.
$R$ : Write the equivalent or total resistance of the entire circuit. In the blanks across from $R_{1}$ under
$V:$ Write the voltage drop across $R_{1}$
I: Write the current flowing through $R_{1}$.
$R:$ Write the resistance of $R_{1} .$
In the blanks across from $R_{2}, R_{3}, \ldots,$ fill in the appropriate numbers under $V, I,$ and
$R$. (Begin by looking for key information given in the table and work from there.)
$$
\begin{array}{cccc}
& \boldsymbol{V} & \boldsymbol{I} & \boldsymbol{R} \\
\hline \text { Battery } & \mathrm{V} & \mathrm{A} & \Omega \\
R_{1} & 12.0 \mathrm{~V} & \mathrm{~A} & 2.00 \Omega \\
R_{2} & \mathrm{~V} & \mathrm{~A} & 4.00 \Omega \\
R_{3} & 24.0 \mathrm{~V} & \mathrm{~A} & 4.00 \Omega \\
R_{4} & \mathrm{~V} & \mathrm{~A} & 8.00 \Omega
\end{array}
$$

Key Concepts

Voltage Drop

Voltage drop refers to the reduction in voltage across a component in a circuit as current flows through it. In series circuits, the battery's total voltage is divided among the resistors proportionally according to their resistances. The voltage drop across each resistor is crucial for understanding energy distribution in the circuit and for verifying that Kirchhoff’s Voltage Law is satisfied.

Battery EMF

Battery electromotive force (EMF) represents the potential difference provided by the battery when no current is flowing in the circuit. It is the initial voltage supplied by the battery that drives the current through the circuit. Understanding the EMF is essential as it is used as the reference voltage from which voltage drops across the various circuit elements are calculated.

Equivalent Resistance

Equivalent resistance is the overall resistance that a circuit or a combination of resistors presents to the source. In series circuits, it is calculated by simply adding the resistances of all components, whereas in parallel circuits, it is found by taking the reciprocal of the sum of the reciprocals of the resistances. This concept is essential for determining the current drawn from a source and for simplifying complex circuits.

Series Circuits

In series circuits, electrical components are connected end-to-end so that there is only one path for current flow. The same current passes sequentially through each component, and the total or equivalent resistance of the circuit is the sum of the individual resistances. Additionally, the supplied voltage from the battery is divided among the series-connected elements depending on their resistances.

Ohm's Law

Ohm's Law is the relationship between voltage, current, and resistance in an electrical circuit, stated as V = I × R. This principle is fundamental for analyzing circuits, as it allows the calculation of one quantity when the other two are known, enabling the determination of voltage drops across components or the current flowing through them.

Parallel Circuits

In parallel circuits, components are connected across the same two nodes, providing multiple paths for the current to flow. Each component experiences the same voltage across it as that supplied by the source, while the total current in the circuit is the sum of the currents through each parallel branch. The calculation of equivalent resistance in parallel circuits involves the reciprocal of the sum of the reciprocals of the individual resistances.

Transcript

00:01 Some practice with omslaw and series versus parallel circuits.

00:05 So in this circuit, we have a battery and for resistors, which are all hooked up in parallel.

00:13 So i'm showing they are in parallel by using the color red.

00:18 And we're starting with a table where we have to identify the voltage and current and resistance of each element.

00:28 With some initial clues given.

00:32 So the initial clues that i show are in blue.

00:36 And what we know to be true is that if objects are in parallel, if resistors are in parallel or any element, really, the voltage difference across them has to be the same.

00:49 So parallel means same delta v, and series means same current.

01:01 And fortunately there's nothing too complicated with the arrangement of resistors.

01:07 They are all in parallel.

01:10 R1 is in parallel with r2 and r3 is in parallel with r4.

01:17 So what we know is that r2 must have the same potential difference across it compared to r1.

01:27 So we can fill that in.

01:29 And i'm showing with the red that i'm using a parallel clue.

01:36 And the same with r4.

01:37 It must have 24 volts.

01:41 And i can come over to the circuit and show we have 24 volts across the bottom parallel configuration and 12 volts across the top.

01:54 And there's nothing else in between.

01:56 So that clue set of clues gives away that we have.