A 24 V emf is connected to terminals A and B in the following circuit. Find the current in each

step 1 calculate the current which passes through each resistance. So for the simplicity, let's label r

A 24 V emf is connected to terminals A and B in the...

Key Concepts

Equivalent Resistance

Equivalent resistance is the total resistance that can replace a combination of resistors in a circuit without changing the overall current and voltage characteristics. This concept is used to simplify calculations in circuits with series-parallel networks by reducing multiple resistors into a single resistor with an effective resistance value.

Ohm's Law

Ohm's Law is a fundamental principle in electric circuits which states that the voltage across a resistor is proportional to the current flowing through it, with the constant of proportionality being the resistance (V = IR). This law is essential for calculating current distribution in circuits when the voltage and resistance are known.

Kirchhoff's Voltage Law (KVL)

Kirchhoff's Voltage Law states that the algebraic sum of all the voltages around any closed loop in a circuit must equal zero. This principle is crucial for analyzing circuits by writing equations for the sum of voltage drops and sources in individual loops, facilitating the calculation of unknown currents or voltages.

Kirchhoff's Current Law (KCL)

Kirchhoff's Current Law asserts that the total current entering a junction must equal the total current leaving the junction. This conservation of charge principle is essential when analyzing complex circuits, as it helps in setting up equations that define the relationships between different currents at circuit nodes.

Series and Parallel Resistor Networks

Understanding series and parallel resistor configurations is key in circuit analysis. Components in series have the same current but their resistances add up, whereas parallel components share the same voltage across them, and their equivalent resistance is determined by the reciprocal sum of the individual resistances. This concept allows one to simplify a complex circuit into an equivalent circuit for easier analysis.

Transcript

00:01 Calculate the current which passes through each resistance.

00:05 So for the simplicity, let's label resistances as r1, r2, r3, r4, and r5 respectively.

00:17 And now we have to draw the equivalent circuit.

00:22 So let's presume that current passes from a to b.

00:28 In this scenario, the equivalent circuit would look like the following so r1 is in series with the section which is r2 and r3 which are in parallel with r4 and additionally it's all in series with r5 and it's all connected to the battery with the voltage of with the emf of 24 volts so let's calculate the total resistance of this circuit.

01:21 So total resistance of this circuit equals to r1 plus r5 plus rx, where rx is a resistance of the middle section.

01:35 So now we have to calculate rx.

01:43 Rx, yeah, 1 over rx equals to 1 over r4 plus, plus 1 over r2 plus r3 because r2 and r3 are connected in series.

02:06 And r4 is in parallel to r2 and r3.

02:11 So now let's modify this expression a little bit.

02:29 So rx, the resistance of the middle part equals to r4, multiplied by r2 plus r3.

02:38 Divided by the sum of these resistances.

02:45 So now we can calculate the total resistance.

02:50 It equals to r1 plus r5 plus this fraction.

03:08 Let's do this calculate.

03:10 Yeah, let's calculate total resistance numerically.

03:14 So it equals to 1 om plus 3 oms.