As shown in the figure, a circuit consists of an emf source with V=20.0 V and six resistors. Re

As shown in the figure, a circuit consists of an emf source...

As shown in the figure, a circuit consists of an emf source with $V=20.0 \mathrm{~V}$ and six resistors. Resistors $R_{1}=5.00 \Omega$ and $R_{2}=10.00 \Omega$ are connected in series. Resistors $R_{3}=$ $5.00 \Omega$ and $R_{4}=5.00 \Omega$ are connected in parallel and are in series with $R_{1}$ and $R_{2}$. Resistors $R_{5}=2.00 \Omega$ and $R_{6}=2.00 \Omega$ are connected in parallel and are also in series with $R_{1}$ and $R_{2}$. a) What is the potential drop across each resistor? b) How much current flows through each resistor?

As shown in the figure, a circuit consists of an emf source with $V=20.0 \mathrm{~V}$ and six resistors. Resistors $R_{1}=5.00 \Omega$ and $R_{2}=10.00 \Omega$ are connected in series. Resistors $R_{3}=$ $5.00 \Omega$ and $R_{4}=5.00 \Omega$ are connected in parallel and are in series with $R_{1}$ and $R_{2}$. Resistors $R_{5}=2.00 \Omega$ and $R_{6}=2.00 \Omega$ are connected in parallel and are also in series with $R_{1}$ and $R_{2}$.
a) What is the potential drop across each resistor?
b) How much current flows through each resistor?

Key Concepts

Current Division

The current division principle applies to parallel circuits, where the total current splits between branches according to their resistances. In a parallel configuration, branches with lower resistance draw a larger portion of the total current. Understanding this concept is vital for accurately determining the current flowing through each component in a circuit with parallel elements.

Equivalent Resistance

Equivalent resistance involves replacing a group of resistors with a single resistor that has the same effect on the overall circuit, making analysis simpler. For series circuits, the equivalent resistance is the sum of the resistances, while for parallel circuits, it is found using the reciprocal formula. This concept allows for the breakdown of intricate resistor networks into simpler, manageable parts.

Voltage Divider Rule

The voltage divider rule is a useful tool for determining the voltage drop across a resistor in a series circuit. It states that the voltage across any resistor in a series network is a fraction of the total voltage, determined by the ratio of that resistor's value to the total series resistance. This rule is fundamental for calculating the potential differences in circuits with series-connected components.

Series Circuit

In a series circuit, components are connected one after the other so that the same current flows through each element consecutively. The total resistance in a series arrangement is the sum of the individual resistances, and the voltage provided by the source is divided among the resistors according to their resistances. This concept is key when calculating voltage drops and current flow in circuits with sequentially connected elements.

Ohm's Law

Ohm's Law is a fundamental principle in electrical circuits that states the voltage across a resistor is directly proportional to the current passing through it, with the resistance being the constant of proportionality. This law, expressed as V = IR, is essential for analyzing the behavior of individual circuit elements and determining how current and voltage are related in any electrical network.

Parallel Circuit

A parallel circuit features components that are connected across the same two points, so they each experience the same voltage drop. The total current from the source divides among the parallel branches according to their resistances, with lower resistance branches carrying higher currents. Calculating the effective resistance of parallel elements is crucial for simplifying and analyzing complex circuits.

Transcript

00:01 In the given problem, there are various resistors joined in mixed grouping.

00:10 First of all here this is r1 which is in series with r2, then two resistors are in parallel with each other and this parallel combination is in series with r1 and r2.

00:25 The upper one are 3, the lower one are 4.

00:29 And then one more parallel combination of two resistors and this parallel combination is in series with the other one upper one r5 lower one r6 and finally a source of voltage and circuit is closed this voltage applied is having a value 20 .0 1 now the values of resistances r1 is 5 .00 om.

01:09 R2 is 10 .0 om.

01:13 R3 is again 5 .00 om.

01:19 R4, 5 .00 om, r5 .00 om, r5, 2 .00 om.

01:30 And finally r5.

01:31 This is also 2 .00 oom now in the first part of the problem after finding the equivalent resistance of this combination we have to find the potential drops across each and every resistance so first of all there are two parallel combination first of all this r3 with r4 and r5 with r6 the net resistances are assumed to be if we consider the terminal terminals here this is a b c and the mid one d and finally this is e.

02:20 So the resistance of this parallel combination will be named as r -c -d and here this last one will be named as r -d -d.

02:37 Now as r3 and r4 are in parallel and having identical resistor each having a value of 5 om therefore the net combination parallel combination rcd will be given by 5 .00 by 2 om means this is 2 .50 om similarly as rr as r as r as r as r r5 and r6 are in parallel and they are also having identical resistor each having same value of 2 .00 om so their parallel combination will come out to be rde is equal to 2 .00 om divided by 2 which comes out to be 1 .00 om.

03:40 Finally is r1, r2, rcd and rde all 4.

03:46 Are in series...

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