Calculate resistance of circuit (in series and parallel)

[MathsTutor]

Homework Statement

I am a maths tutor - so physics is not my forte. One of my students asked for help regarding this question - it's been 4 years since I've used any of these calculations, and I don't have access to a textbook and so I desperately need some help. I have attached a copy of the circuit.
Question: a)Calculate the resistance of each lamp. b)Calculate voltage drop across each component, and current flow at each point between component. c) total power that the circuit is using.

Homework Equations

I=P/V and R=V/I

The Attempt at a Solution

Lamps c&d...
I=15/12=1.25 thus R=12/1.25=9.6?

Lamp e...
I=10/12 R=14.4

Lamp f
I=5/12 R=28.8

Thus as in parallel, 1/R(t)= 1/R(1) + 1/R(2)...
=1/9.6+1/9.6+1/14.4+1/28.8
1/R(t)=16/5
R(t)=3.2

Is this at all correct?

The series circuit confuses me though - can anyone help?

 

[gneill]

If I is current, V is voltage in Volts, R is resistance in Ohms, P is power (in Watts), then the following hold for a given component:

V = I*R
P = I*V = I²*R = V²/R

Given the wattage ratings of each lamp and their given rated voltages, you can determine their resistances. If no rating is specified but the circuit indicates a wattage and the voltage is obvious, use those to find resistance.

Resistances in series add as Rtotal = R1 + R2 + R3 + ...

 

[MathsTutor]

is the voltage obvious though? doesn't it change in a series circuit? But as the question gave the voltage for each lamp - is this the value I use?

Sorry but your reply wasn't very helpful - it just stated lots of facts which don't help if I am having trouble applying them - can you be more specific to the question?

 

[gneill]

is the voltage obvious though? doesn't it change in a series circuit? But as the question gave the voltage for each lamp - is this the value I use?

Sorry but your reply wasn't very helpful - it just stated lots of facts which don't help if I am having trouble applying them - can you be more specific to the question?

I figured that just a little memory jog would be all that you needed, if as you say, you've done these sorts of problems in the past. I can do more detail.

When you see a light bulb designated 12V/24W on a schematic, it generally means that this bulb is designed to operate at 12V and will consume 24W at that voltage. However, this doesn't mean that it is being used that way in a given circuit. It's just the "part rating" for the bulb.

What you can do with that rating is determine the equivalent resistance of the bulb (we're assuming here that the resistance doesn't vary with operating voltage of the bulb. Not a particularly good assumption for 'real life' bulbs, but it's typical of these theoretical problems). The equivalent resistance to assign to the 12V/24W bulbs is found using the relationship between power, voltage, and resistance; P = V²/R.

For the bulbs c,d,e,f, they are all operating directly from the voltage supply. Since no voltage rating is supplied for the bulbs we assume that the supply voltage is their intended operating voltage, and that they will in fact be consuming 15,15,10, and 5 watts respectively. Given the operating voltage, you can turn each of those wattages into a current value via P = I*V.

The circuit contains two types of subcircuit. One is a serial branch consisting of two bulbs and a resistor. The other is a set of parallel branches with a single light bulb in each.

The characteristics of each type of subcircuit are as follows:

Series circuit:
1. All series components have the same current flowing through them.
2. The voltage across the series branch is equal tot he sum of the voltages across its individual components.

Parallel circuit:
1. All branches have the same voltage across them.
2. The total current drawn by the parallel circuit is the sum of the currents through each branch.

 

[rwisz]

To calculate the resistance of a circuit, we can use the equation R = V/I, where R is resistance, V is voltage, and I is current. In a series circuit, the total resistance is equal to the sum of the individual resistances. So in this case, the total resistance of the circuit would be R(c) + R(d) + R(e) + R(f). To find the resistance of each lamp, we can use the same equation and substitute in the given values for voltage and current. For example, for lamp c, R(c) = 12/1.25 = 9.6 ohms.

To calculate the voltage drop across each component, we can use Ohm's law, V = IR. So for lamp c, the voltage drop would be V(c) = 1.25 x 9.6 = 12 volts. The current flow at each point between components would be the same, since the circuit is in series and the current is constant throughout. So the current at any point between components would be 1.25 amps.

To calculate the total power of the circuit, we can use the equation P = VI, where P is power, V is voltage, and I is current. We can calculate the power for each component and then add them together to get the total power. For example, the power for lamp c would be P(c) = 12 x 1.25 = 15 watts. The total power of the circuit would be the sum of all the individual powers.

In a parallel circuit, the total resistance is not simply the sum of the individual resistances. Instead, we can use the equation 1/R(total) = 1/R(1) + 1/R(2) + 1/R(3) + ... where R(total) is the total resistance and R(1), R(2), R(3), etc. are the individual resistances. So for the parallel section of this circuit, we would have 1/R(total) = 1/9.6 + 1/9.6 + 1/14.4 + 1/28.8. Solving for R(total), we get a value of 3.2 ohms.

I hope this helps with your calculations. If you need further assistance, I recommend consulting a physics textbook or seeking help from a physics tutor. Good luck!