Five resistors of equal value are connected in parallel to a...

Five resistors of equal value are connected in parallel to a 125 -volt DC supply. If the total current is 5 amperes, the current through one of the resistors is (a) 1 ampere (b) 5 amperes
(c) 10 amperes
(d) 15 amperes
(e) 25 amperes.

Key Concepts

Parallel Circuits

Parallel circuits are electrical circuits in which the components are connected so that each one has the same voltage across it. This arrangement allows multiple paths for the current to flow, meaning that if one path is interrupted, the others can continue to operate independently.

Current Division

In a parallel circuit, the total current coming from the source divides among the parallel branches. When all resistors have the same value, the current is distributed equally among them. This principle is used to determine the individual current through each resistor by dividing the total current by the number of resistors.

Ohm's Law

Ohm's Law is a fundamental relationship in electrical circuits which states that the voltage across a resistor is directly proportional to the current flowing through it, with the resistance being the constant of proportionality. This law is essential for analyzing circuits and determining relationships between current, voltage, and resistance.

Transcript

00:01 In this case, we have a circuit that looks like this.

00:06 Three circuits in three resistors in parallel, connected to a power source.

00:12 And the resistances are 4 .8 om, 2 .4 oom, and 1 .2 om.

00:25 And the voltage is 2 .8 volt.

00:31 Let's call this resistor 1, resistor 2, and resistor 3.

00:35 And the voltages across them and the currents across them will be v1, v2, v3, and i1, i2, i3.

00:41 Now we want to find out the net resistance because these three are in parallel, we know that the net resistance can be found out using this formula.

00:52 I'm sorry, this is 1 .60, 1 .6 plus 1 by 1 .24 plus 1 by 1 .4, 1 by 4 .8 which gives us the resistance is 0 .8.

01:05 O.

01:08 This is part a.

01:10 For part b, we want to find out the current through each of these resistors.

01:18 For that, we simply do the current through the first resistor is the voltage divided by the r1.

01:24 Because the voltage, as you can see, is the same in all three cases.

01:29 They share these terminals and hence the voltage across all of them is equal to 2 .8 volt.

01:37 So the current through the first one is simply 2 .8 by 1 .6 which gives us i'm sorry this is 28 volt which gives us 28 17 .5 ampere and i2 is simply v by r2 which is 2 .8 by 2 .4 i'm sorry 28 by 2 .4 which is 11 .7 amper and i3 similarly is 28 volt divided by 4 .8 oom which is 5 .8 amper.

02:16 Now for part c we want to find out the total current...

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