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Math Help - total resistance, potential difference & current in series & parallel dc circuits

  1. #1
    Junior Member turbod15b's Avatar
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    total resistance, potential difference & current in series & parallel dc circuits

    Series circuit connected to a d.c power supply of 12volts

    R1 300ohms
    R2 480ohms
    R3 220ohms

    is the total resistance 1000ohms?

    is the total circuit supply current, 12/1000=0.012A?

    the potential difference in volts across EACH resistor?

    R1 300*0.012=3.6v?
    R2 480*0.012=5.76v?
    R3 220*0.012=2.64v?

    3.6+5.76+2.64=12v?

    Parallel circuit connected to a d.c power supply of 12volts

    how do i calculate the total circuit resistance?
    is it 300+480+220=1000ohms?

    how do i calculate the total circuit supply current?

    is this how to calculate the current through each resistor?
    12v/300=0.04A
    12v/480=0.025A
    12v/220=0.054A

    total= 0.119A?

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  2. #2
    Super Member
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    Quote Originally Posted by turbod15b View Post
    Series circuit connected to a d.c power supply of 12volts

    R1 300ohms
    R2 480ohms
    R3 220ohms

    is the total resistance 1000ohms?

    is the total circuit supply current, 12/1000=0.012A?

    the potential difference in volts across EACH resistor?

    R1 300*0.012=3.6v?
    R2 480*0.012=5.76v?
    R3 220*0.012=2.64v?

    3.6+5.76+2.64=12v?

    Parallel circuit connected to a d.c power supply of 12volts

    how do i calculate the total circuit resistance?
    is it 300+480+220=1000ohms?

    how do i calculate the total circuit supply current?

    is this how to calculate the current through each resistor?
    12v/300=0.04A
    12v/480=0.025A
    12v/220=0.054A

    total= 0.119A?

    Hello,

    all your results are OK.

    You know the total of the circuit current (0.119 A) and you know the total voltage (12 V), thus you can calculate the total resistance:
    R_{total}=\frac{12V}{0.119A}=100,4\Omega

    The general formula to calculate the total resistance in a parallel circuit is:

    \frac{1}{R_{total}}=\frac{1}{R_1}+\frac{1}{R_2}+\f  rac{1}{R_3}...

    EB
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  3. #3
    Junior Member turbod15b's Avatar
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    so the total circuit resistance in PARALLEL is 12v/0.119=100.84
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  4. #4
    Super Member
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    Quote Originally Posted by turbod15b View Post
    so the total circuit resistance in PARALLEL is 12v/0.119=100.84
    Hello,

    correct!

    Only to show you that the formula which I've written the previous post will give the same result:

    \frac{1}{R_{total}}=\frac{1}{300}+\frac{1}{480}+\f  rac{1}{220}=\frac{263}{26400}

    Now calculate the reziprocal(?) value and you'll get:

    R=\frac{26400}{263} \approx 100.380228..

    You have to add the right units of course!

    EB
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  5. #5
    Junior Member turbod15b's Avatar
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    how u get 263 and 26400
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  6. #6
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    Quote Originally Posted by turbod15b View Post
    how u get 263 and 26400
    Hello,

    to add fractions you have to use a common denominator, which is the LCM of 300, 480, 220. I used prime number factorization:

    300 = 2*2*3*5*5

    480 = 2*2*2*2*2*3*5

    220 = 2*2*5*11

    denominator = 2*2*3*5*(5)*(2*2*2)*(11) = 26400

    Multiply the numerator of each fraction so that the denominator of each fraction becomes 26400:

    \frac{1}{300}+\frac{1}{480}+\frac{1}{220}=<br />
\frac{1}{300}\cdot \frac{88}{88}+\frac{1}{480}\cdot \frac{55}{55}+\frac{1}{220}\cdot \frac{120}{120}=\frac{263}{26400}

    EB
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