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# Physics - resistance question watch

1. Slightly stuck on one of the parts on two questions. Sorry if it's quite a lengthy post but I feel as if I should write down the whole two questions and the parts with it to make sense. I've also included my answers too and I've mentioned what I need help on.

Question 1. A circuit in a hair dryer consists of a small motor with a voltage of 12 V in series with a heating coil. Both are connected to a 240 V power supply. Current flowing through the motor is 0.6 A.
a) calculate the resistance of the motor.
b) What is the current in the heating coil? and calculate its resistance.

a) I got 20 Ω
b) The current through the heating coil is 0.6 A (the same as the current going through the motor) because in series current flowing through one component is the same as the current going through the next component (correct me if I'm wrong).
For the resistance I got 380 Ω but I don't think that's right for some reason... I hope someone can verify this for me.

Question 2: The resistance of a heating element in 450 000 Ω and it's connected to a main supply of 240 V.
a) what's the current flowing through it?
b) how many coulombs of charge pass through the heating element in 1 minute?
c) how much energy is transferred to each coulomb of charge?
d) how much heat energy is produced by the coil in 1 minute?

a) I got 0.000533 A
b) I'm not sure if this is right but I got 0.032 C
c) I'm not sure this is right either but I got 7.68 J.
d) I'm stuck on this and I have no idea what to do :/
2. (Original post by minibuttons)
Slightly stuck on one of the parts on two questions. Sorry if it's quite a lengthy post but I feel as if I should write down the whole two questions and the parts with it to make sense. I've also included my answers too and I've mentioned what I need help on.

Question 1. A circuit in a hair dryer consists of a small motor with a voltage of 12 V in series with a heating coil. Both are connected to a 240 V power supply. Current flowing through the motor is 0.6 A.
a) calculate the resistance of the motor.
b) What is the current in the heating coil? and calculate its resistance.

a) I got 20 Ω
b) The current through the heating coil is 0.6 A (the same as the current going through the motor) because in series current flowing through one component is the same as the current going through the next component (correct me if I'm wrong).
For the resistance I got 380 Ω but I don't think that's right for some reason... I hope someone can verify this for me.

Question 2: The resistance of a heating element in 450 000 Ω and it's connected to a main supply of 240 V.
a) what's the current flowing through it?
b) how many coulombs of charge pass through the heating element in 1 minute?
c) how much energy is transferred to each coulomb of charge?
d) how much heat energy is produced by the coil in 1 minute?

a) I got 0.000533 A
b) I'm not sure if this is right but I got 0.032 C
c) I'm not sure this is right either but I got 7.68 J.
d) I'm stuck on this and I have no idea what to do :/
I agree with you on question 1 for both parts except I'm not 100% sure on part b. As it's a heating coil I'd assume it would be non-ohmic because it heats up, however unless they gave you a graph or means of working it out I guess the only possible answer is 380.

On Q2, provided your answer for part a is correct I got the same for part b.

I got a different answer to part c. It says charge per coulomb so I used Work done = Voltage x Charge. It states per coulomb so if it's 1 coulomb and voltage is constant then 240 x 1. However someone might want to clarify my logic on this because it seems too obvious to me and your answer seems more like an answer they'd want for a calculation.

For part d I think you'd need to think of the definition for potential difference, 'energy transfer per unit charge when electrical energy is converted into another form of energy'. Assuming the coil is 100% efficient (unlikely but the only way you can do it) you can use the same work done equation that is above to work out the energy, coincidently (or maybe not ) they asked you to find the charge passing through the heating element in 1 minute.

I hope this helps
3. (Original post by k4l397)
I agree with you on question 1 for both parts except I'm not 100% sure on part b. As it's a heating coil I'd assume it would be non-ohmic because it heats up, however unless they gave you a graph or means of working it out I guess the only possible answer is 380.

On Q2, provided your answer for part a is correct I got the same for part b.

I got a different answer to part c. It says charge per coulomb so I used Work done = Voltage x Charge. It states per coulomb so if it's 1 coulomb and voltage is constant then 240 x 1. However someone might want to clarify my logic on this because it seems too obvious to me and your answer seems more like an answer they'd want for a calculation.

For part d I think you'd need to think of the definition for potential difference, 'energy transfer per unit charge when electrical energy is converted into another form of energy'. Assuming the coil is 100% efficient (unlikely but the only way you can do it) you can use the same work done equation that is above to work out the energy, coincidently (or maybe not ) they asked you to find the charge passing through the heating element in 1 minute.

I hope this helps
for 1b) I worked out the pd across the resistance so I did 240 - 12 = 228V and then with that I worked out the resistance to be 228/0.6 = 380 Ω. It says on the question to use my explanation earlier (where I justified why the current in the heating coil is 0.6 A) - I think this has got to do with Kirchoff's law with the current being the same at every point in the series circuit.
4. (Original post by minibuttons)
for 1b) I worked out the pd across the resistance so I did 240 - 12 = 228V and then with that I worked out the resistance to be 228/0.6 = 380 Ω. It says on the question to use my explanation earlier (where I justified why the current in the heating coil is 0.6 A) - I think this has got to do with Kirchoff's law with the current being the same at every point in the series circuit.
Sounds right to me
5. (Original post by minibuttons)
Q1 a) I got 20 Ω
Correct.

Spoiler:
Show
R = V/I
R = 12/0.6
R = 20 ohms.

(Original post by minibuttons)
Q1 b) The current through the heating coil is 0.6 A (the same as the current going through the motor) because in series current flowing through one component is the same as the current going through the next component (correct me if I'm wrong).
Correct. The current flowing through the circuit is the same at all points in a series circuit path.

(Original post by minibuttons)
For the resistance I got 380 Ω but I don't think that's right for some reason... I hope someone can verify this for me.
Correct. The voltages dropped around a crcuit must sum to the supply voltage. You are told the motor is 12V and the circuit is supplied with 240V:

Spoiler:
Show
Vsupply = Vmotor + Vheater
Vheater = Vsupply - Vmotor
Vheater = 240 - 12
Vheater = 228 Volts.

Rheater = Vheater/Iheater
Rheater = 228/0.6
Rheater = 380 ohms.

(Original post by minibuttons)
Question 2: The resistance of a heating element in 450 000 Ω and it's connected to a main supply of 240 V.
a) what's the current flowing through it?
b) how many coulombs of charge pass through the heating element in 1 minute?
c) how much energy is transferred to each coulomb of charge?
d) how much heat energy is produced by the coil in 1 minute?
(Original post by minibuttons)
a) I got 0.000533 A
Correct. Although you will not get penalised, it's good practice to quote the answer in exponential form as many zero's ater the decimal point can be a source of error.

Spoiler:
Show
I = V/R
I = 240/450x103
I = 0.533x10-3 A or 0.533 mA.

(Original post by minibuttons)
b) I'm not sure if this is right but I got 0.032 C
Correct.

Spoiler:
Show
Q = I x t
Q = 0.533x10-3 x 60
Q = 0.032 Coulombs

(Original post by minibuttons)
c) I'm not sure this is right either but I got 7.68 J.
Incorrect.

Voltage is defined as Joules per Coulomb of charge.

Spoiler:
Show
V = E/Q
E = V x Q and since Q = 1 Coulomb by defintion
E = 240 x 1
E = 240 Joules.

i.e. 240 Volts means 240 Joules of energy in every Coulomb of charge.

This is a very important definition.

(Original post by minibuttons)
d) How much heat energy is produced in the coil in 1 minute? I'm stuck on this and I have no idea what to do :/
By definition Joules = Watt seconds.

You are given the time. You need to find the power developed by the heating coil. You should know the equation relating voltage and current to power in an electrical circuit.

E = Power x time
E = Pt..................eq(1)

Spoiler:
Show
in an electrical circuit:

P = VI. Substituting for P in eq(1) above:

E = VIt

E = 240 x 0.533x10-3 x 60

E = 7.68 Joules (2 d.p.)
6. (Original post by uberteknik)

Incorrect.

Voltage is defined as Joules per Coulomb of charge.

Spoiler:
Show
V = E/Q
E = V x Q and since Q = 1 Coulomb by defintion
E = 240 x 1
E = 240 Joules.

i.e. 240 Volts means 240 Joules of energy in every Coulomb of charge.

This is a very important definition.

By definition Joules = Watt seconds.

You are given the time. You need to find the power developed by the heating coil. You should know the equation relating voltage and current to power in an electrical circuit.

E = Power x time
E = Pt..................eq(1)

Spoiler:
Show
in an electrical circuit:

P = VI. Substituting for P in eq(1) above:

E = VIt

E = 240 x 0.533x10-3 x 60

E = 7.68 Joules (2 d.p.)
Thank you so much for helping me out on the last two questions
7. (Original post by minibuttons)
Thank you so much for helping me out on the last two questions

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