If resistors are connected in series & parallel what will be the power?

Question

If resistors are connected in series & parallel what will be the power?

If resistors are connected in series & parallel what will be the Current?

If resistors are connected in series & parallel what will be the voltage?

If resistors are connected in series & parallel what will be the resistance?

If battery are connected in series & parallel what will be the voltage, current, power?

Answer 1

Okay, first, you need to have a solid conceptual understanding of current and voltage.

Voltage is between two points. So if two resistors are connected between the same two points (in parallel), they will both experience the same voltage.

Current is through a point. So it two resistors are connected in series, all the current that goes through the first one goes through the second one (since it has no place else to go, and they are connected at a point that has some particular amount of current going through it). If two resistors are connected in series, all the current that goes through one must go through the other.

Parallel -> equal voltage

Series -> equal current

For a resistor, R=V/I, so given the voltage you can find the current, given the current, you can find the voltage.

R=V/I V=IR I=V/R

Also, for power, P=VI. Combining, you get P=V^2 / R and P=I^2 * R.

So let's start with resistors in series. They will both experience the same current. The voltage across each will be that current times the resistance. The power dissipated by each will be that current squared times the resistance.

For resistors in parallel, they will both be across the same voltage. The current through each will be that voltage divided by the resistance. The power will be that voltage squared divided by the resistance.

For batteries connected in parallel, their voltage must be the same. It is an illegal configuration to connect two ideal batteries of different voltages in parallel (by definition, an ideal battery does whatever it takes to make the voltage across its ends its specified voltage). The current will be the same because the current is determined by the voltage supplied. The power will be the same as well.

For batteries connected in series, the voltage will be the sum of the voltages of the batteries connected. Typically, the current will be more, because I=V/R and V goes up. Typically the power will be more, P=V^2 / R and V goes up. (I say 'typically' because I"m assuming a resistive load. Obviously, if more voltage blows a fuse or something weird like that, power won't go up.)

It's most important that you grasp the fundamental notion that current is 'through' some end of a wire/component and voltage is 'across' two points.

Answer 2

To simplify calculation let's assume we have 2 x 10ohm resistors and 2 x 10 volt batteries capable of supplying 1 amp

each.(B1 and B2)

If the 2 resistors (R1 and R2) are connected in series to one of the batteries:

The current will be  I = V / R  ie   0.5  = 10 / 20 Amps

The power will be   P = V * I  ie     5   = 10 * 0.5 Watts

The voltage across  each resistor wil be  V = I * R

  ie  5  =  0.5 * 10 volts

The total resistance wil be R1 + R2  ie 10 + 10  = 20 Ohms

If the two resistors are connected in parallel across one of the batteries:

The total resistance will be (R1 * R2)  / (R1 + R2)

ie 100 / 20 = 5 ohms

The Voltage across both resistors wil be  10 Volts

The current through each resistor wil be :

I1 = V / R1 and I2 = V / R2   ie  10 / 10 = 1 Amp

The total current will be I1 + I2   ie 1 + 1 = 2 Amps

The power in each resistor will be:

P1 = V * I1 and P2 = V * I2  ie 10 * 1 = 10 Watts

The total power will be  P1 + P2 ie 10 + 10 = 20 Watts

In the case of the two batteries connected in series:

The voltage will be  VB1 + VB2 = 10 + 10 = 20 Volts

The current available will be 1 amp

The power available will be  P = Vtotal * Itotal

ie P = 20 * 1 = 20 Watts

In the case of the 2 batteries connected in parallel:

the Voltage will be 10 Volts

The current available will be IB1 + IB2 = 1 + 1 = 2 Amps

The power available will be

PB1 = VB1 * IB1 ie 10 * 1 = 10 Watts

and  

PB2 = VB1 * IB2  ie 10 * 1 = 10 Watts.

The total power available will be PB1 + PB2  Watts

ie  10 + 10 = 20 Watts

Answer 3

doesn't matter, series or parallel, P = E*I and I = E/R applies to each resistor.

For a bunch of resistors in series, the current is equal in each, and the voltages add up.

For a bunch of resistors in parallel, the voltage is the same across each, and the currents add up.

Answer 4

connected in series:

R=r+r'+r"+..

I=V/R

devide the total voltage into the the total resistance(calculated by the above formulla)to calculate total current. current for each resistor is equal with this total current.

for each resistor potetial difference(voltage) between two ends is equal with: I.r

total power=R.I.I or (V.V)/R or V.I

power for each resistor is calculated with the same formulla but put  voltage and and resistance of the resistor you want to find the power of,instead of toal v & r.

parallel:

1/R=1/r +1/r' +1/r" +...

voltage for each resistor is equal withthe total voltage.

current for each resistor =v/r

total current V/ R(total)

power is calculated like before. about batteries let's talk later.