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

1. ## 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?

2. Originally Posted by turbod15b
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,

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

3. so the total circuit resistance in PARALLEL is 12v/0.119=100.84

4. Originally Posted by turbod15b
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

5. how u get 263 and 26400

6. Originally Posted by turbod15b
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:

$\frac{1}{300}+\frac{1}{480}+\frac{1}{220}=
\frac{1}{300}\cdot \frac{88}{88}+\frac{1}{480}\cdot \frac{55}{55}+\frac{1}{220}\cdot \frac{120}{120}=\frac{263}{26400}$

EB