(a) What is the equivalent resistance of the circuit shown in Fig. 19-82? [Hint: Redraw the circ

(a) What is the equivalent resistance of the circuit shown...

Key Concepts

Power Dissipation Calculation

Power dissipation in a resistor is the process by which electrical energy is converted into heat. It can be calculated using formulas such as P = I^2 • R or P = V^2 / R. This concept is important for ensuring that components operate within safe thermal limits while effectively managing energy usage in a circuit.

Current Division

Current division refers to the method of determining how the total current entering a parallel circuit divides among the different branches. This technique relies on the inverse relationship between branch resistance and the portion of current flowing through that branch, making it useful for solving circuits with parallel resistors.

Ohm's Law

Ohm’s law is a fundamental electrical principle stating that the voltage across a resistor is directly proportional to the current flowing through it, with the constant of proportionality being the resistance. This relationship, expressed as V = I • R, is essential for analyzing voltage drops, current flow, and resistance in circuits.

Equivalent Resistance

Equivalent resistance is a concept used to simplify complex circuits by combining multiple resistors into a single resistor that has the same effect on the circuit. In circuits with series and parallel combinations, calculating the equivalent resistance allows easier analysis of the overall circuit behavior using Ohm’s law.

Parallel Circuit

A parallel circuit consists of components connected such that there are multiple paths for the current to flow. In a parallel configuration, all components share the same voltage across them, but the total current is divided among the branches. The reciprocal of the equivalent resistance is the sum of the reciprocals of the individual resistances.

Series Circuit

A series circuit is one where electrical components are connected end-to-end in a single path, so the same current flows through each component. In such circuits, the total or equivalent resistance is the sum of the individual resistances, and the voltage drop across each resistor is determined by its resistance according to Ohm’s law.

Transcript

00:01 So if we simplify the circuit diagram which is here we get something like this where the 12 oms and 22 oms resistor are in series are in parallel and then 4 .5 ombs register is in series with these two guys and then this whole setup is in parallel connection with 14 oms and let's let's actually call this setup r1 so that it's easier to calculate now the first job for us is to find out this r1 2 value so it's going to be r1 2 which is equal to 1 over 12 oms plus 1 over 22 oms reciprocal of that and that gives us 7 .7 6 5 oms now since this guy is in series connection with 4 .5 so the total and then let's call this guy r3 so the total equivalent resistance will be r1 to 3 which is 4 .5 plus 7 .765 oms which is equal to 12.

01:42 265 oms let's actually make some space here so yeah so now we know this and from there we know that 14 oms is in parallel connection with this whole setup so that's going to be our eq which is parallel so that's going to be one point one over one two six five oh so that's this guy plus one over 14 oms reciprocal of that and that gives us and that gives us 6 .538 oms let me actually represent it properly so that we can understand so now this whole setup we call this r one two three right so that's the equivalent resistance of the whole circuit now for part b we need to find the current that's going through this resistor for denome so what we can do is we can apply kirchups loop rule on this loop and if we do so we see it's going to be shy minus i 1 4 times r14 so i 1 4 is basically the current that's passing to 14 -homes resistor so if we solve for i 1 4 we get something like this and here our emm voltage or shy is given so that's that's how we get our current so now we know that 0 .4286 amps current is going through this part so we need to figure out what amount of current is going through we need to figure out what amount of current is going through r12 and r12 to be precise so what we do here is again we are using kirchap's law loop rule for the outer loop and by outer loop we mean that we take this whole thing and we're considering these two resistor as one.

04:39 So that means instead of writing these two separately, we're writing r1 ,2.

04:45 So that means the current, so that means this guy and this whole thing is in series connection.

04:50 So the current flowing through the setup will be same.

04:55 So that's what we did here...

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