This is not really homework ( I am modifying my DIY heated motorcycle jacket ) but the question is simple enough for textbook homework. But this is not my field and I am confused.
I have a long 32 gauge wire (48 feet) that snakes around my jacket to provide heat. It has 6 ohms of resistance so at 12volts, that is 2 amps and 24 watts of heat.
Now I want to add gloves to this wire. Each glove has 2 ohms of resistance.
If I add the gloves in series that gives me 6 + 2 + 2 = 10 ohms or only 1.2 amps and 14.4 watts of heat which is not nearly enough.
So I want to add the gloves in PARALLEL to give me more heat. This circuit looks like one really long wire (20 feet) with a loop sticking out, then the long wire continues another 20 feet; then the second loop for the other glove.
So I think I have to analyze this circuit in two halves: 3 ohms of long wire with a 2 ohm parallel loop sticking out of the middle. Then the same thing for the other half: a parallel circuit with 2 ohms on one path and 3 ohms on the other path.
That gves me 1.2 ohms for each parallel half (2*3)/(2+3) = 6 / 5
The halves are in series so 2.4 ohms for the whole thing
Hence, 5 amps (12/2.4)
and 60 watts (5 * 12 ) for the whole circuit
I think this part is right - if not, stop me now.
Where I get confused is allocating the total 60 watts to each glove.
The series circuit is symmetric so each half has a 6 volt drop ( 12 /2 )
Each half has 30 watts and 5 amps.
Then I allocate a half (6v, 5a, 30w) among the two parallel resistances of 2 for gloves and 3 for long wire
So one glove is:
18 watts = (E * E) / R = 6volts * 6 volts / 2 ohms
or
3 amps in a glove = E / R = 6 volts / 2 ohms
18 watts = (I * I) * R = 3 amps * 3 amps * 2 ohms
I have obviously simplified the arithmetic BUT are my concepts right??
? This is a mixed circuit of series and parallel
? Partition the circuit into two series pieces
? Calculate the total parallel resistance within each piece
? Add the resistances of each piece together as they are in series
? Calculate the whole circuit
? Take the circuit back apart into its two pieces (now its 6v each)
? Calculate watts for a glove in its piece (half) of the circuit
thank you - my hands are really cold and I hope this is right
I have a long 32 gauge wire (48 feet) that snakes around my jacket to provide heat. It has 6 ohms of resistance so at 12volts, that is 2 amps and 24 watts of heat.
Now I want to add gloves to this wire. Each glove has 2 ohms of resistance.
If I add the gloves in series that gives me 6 + 2 + 2 = 10 ohms or only 1.2 amps and 14.4 watts of heat which is not nearly enough.
So I want to add the gloves in PARALLEL to give me more heat. This circuit looks like one really long wire (20 feet) with a loop sticking out, then the long wire continues another 20 feet; then the second loop for the other glove.
So I think I have to analyze this circuit in two halves: 3 ohms of long wire with a 2 ohm parallel loop sticking out of the middle. Then the same thing for the other half: a parallel circuit with 2 ohms on one path and 3 ohms on the other path.
That gves me 1.2 ohms for each parallel half (2*3)/(2+3) = 6 / 5
The halves are in series so 2.4 ohms for the whole thing
Hence, 5 amps (12/2.4)
and 60 watts (5 * 12 ) for the whole circuit
I think this part is right - if not, stop me now.
Where I get confused is allocating the total 60 watts to each glove.
The series circuit is symmetric so each half has a 6 volt drop ( 12 /2 )
Each half has 30 watts and 5 amps.
Then I allocate a half (6v, 5a, 30w) among the two parallel resistances of 2 for gloves and 3 for long wire
So one glove is:
18 watts = (E * E) / R = 6volts * 6 volts / 2 ohms
or
3 amps in a glove = E / R = 6 volts / 2 ohms
18 watts = (I * I) * R = 3 amps * 3 amps * 2 ohms
I have obviously simplified the arithmetic BUT are my concepts right??
? This is a mixed circuit of series and parallel
? Partition the circuit into two series pieces
? Calculate the total parallel resistance within each piece
? Add the resistances of each piece together as they are in series
? Calculate the whole circuit
? Take the circuit back apart into its two pieces (now its 6v each)
? Calculate watts for a glove in its piece (half) of the circuit
thank you - my hands are really cold and I hope this is right