Derivation of series parallel circuit resistance, voltage current distribution, power distribution

String: r=r1+r2 The total resistance value of the series circuit is equal to the sum of the resistance values of each resistance.

r=u/ir=u1+u2/i }r=u1/i +u2/i =r1+r2

u=u1+u2 ∵i=i1=12

u1/u2=r1/r2

u=ir→u1/u2=i1r1/i2r2 ∵ i=i1=i2 ∴u1/u2=r1/r2

p1/p2=r1/r2

p=i²r p1/p2=i²r1/i²r2 ∵i=i1=i2 ∴ p1/p1=r1/r2

Combine. 1/r=1/r①+1/r②

r=u/iu=u1=u2

1/r=u/i1+i2

1/r=u/i1+u/i2

1/r=1/r①=1/r②

i1/i2=r1/r2

u=i1r1=i2r2

i1/12=r2/r1

p1/p2=r2/r1

p=u²/r

p1/p2=u²/r1/u²/r2=r2/r1

Is it the second line that was launched?

Series: The current is equal So the ratio of u is only related to r in i and r The same is true for p, p=ui is related to u, and u is related (proportional) to r

Parallel: The voltage is equal i=u r r, the larger i is, the smaller i is, so it is inversely proportional to p u u r and also inversely proportional to r.

With a good grasp of these formulas, these formulas can be derived: in a series circuit, the current of each component is equal; In a parallel circuit, the voltages at both ends of each component are equal.

In a series circuit, the ratio of voltage, electrical work and electrical power is equal to the ratio of resistance except for current.

u1 u2=w1 w2=p1 p2=r1 r2=q1 q2 voltage, electrical work, electric power, resistance, electric heat).

and i1 = i2 (current).

Series circuits. Current: The current is equal everywhere in the series circuit.

Parallel circuits. Current: In a parallel circuit, the current in the dry circuit is equal to the sum of the currents in each branch.

Voltage of the series circuit: In the series circuit, the sum of the voltages of the parts of the circuit is equal to the total voltage.

Voltage of parallel circuit: In parallel circuit, the voltage at both ends of each branch is equal.

In a resistor parallel circuit, the power () allocated to each resistor ().

a.It is directly proportional to the resistance of the great prudence and the small mind.

b.It has nothing to do with the size of the resistance.

c.It is inversely proportional to the magnitude of the resistance.

d.It is proportional to the square of the electrical service clearance.

Correct answer: c

Question 2: From the meaning of the title, it can be seen that the voltage of the two bright and coarse ends of the resistor is u1 is* r 1 amp * 1 oh 1 volt (left positive and right negative).

Then the voltage at both ends of the available current source is u2, u1, us 1 volt, 5 volts, and 6 volts (up, positive, and negative).

So the output power of the current source is P2 IS*U2 1 Amp*6 Volts 6 Watts.

Question 3: From the meaning of the title, it can be seen that the voltage at both ends of the 1 ohm resistor is u1 is right* r1 1 amp * 1 ohm 1 volt (negative at the top and positive at the bottom).

Then the voltage at both ends of the 1 amp current source on the right side is u2 us u1 5 volts 1 volt 4 volts (negative at the top and positive at the bottom).

So the power emitted by the 1A current source in the diagram is P2 is right*U2 1 Amp*4 volts 4 watts.

Electrical power. It refers to the physical quantity of how fast or slow the work done by the current is.

The calculation formula is: p=ui.It doesn't matter if it's a series circuit or a parallel circuit.

Series circuits.

The current of each branch is the same as i, and the sum of the voltages of each branch is the total voltage: U (total) = U1 + U2 + .

U (Total) * i = P (Total), U (Total) Noise Swift = U1 + U2 + .

It can be obtained: p(total)=u(total)*i=(rush this u1+u2+...)i=u1*i+u2*i+..p1+p2+..

That is, the total power of the series circuit is equal to the sum of the power of each distribution in the circuit, which is rooted in Kirchhoff's voltage law kvl

The parallel circuit hits the ---

The voltage of each branch is the same as U, and the sum of the currents of each branch is the total current: i (total) = i1 + i2 + .

i(total)*u=p(total),i(total)=i1+i2+..,

It can be obtained: p(total)=i(total)*u=(i1+i2+..u=i1*u+i2*u+..p1+p2+..

That is, the total power of the parallel circuit is equal to the sum of the power of each distribution in the circuit, which is rooted in Kirchhoff's current law kcl

1 i = u r (Ohm's law: the current in a conductor is proportional to the voltage across the conductor and inversely proportional to the resistance of the conductor).

2． i=i1=i2=…=in (characteristic of the current in a series circuit: the currents are equal everywhere).

3． u=u1+u2+…+un (characteristic of voltage in series circuits: in series circuits, the total voltage is equal to the sum of the voltages at both ends of each part of the circuit).

4． i=i1+i2+…+in (characteristics of the current in a parallel circuit: the current on the main circuit is equal to the sum of the currents in each branch).

5． u=u1=u2=…=un (Characteristics of voltage in parallel circuits: The voltage at both ends of each branch is equal. are equal to the supply voltage).

6． r=r1+r2+…+rn (characteristic of resistance in series circuits: the total resistance is equal to the sum of the resistances of the parts of the circuit).

7． 1/r=1/r1+1/r2+…+1 rn (characteristic of resistors in parallel circuits: the reciprocal of the total resistors is equal to the sum of the reciprocals of the various parallel resistors).

8 r and = r n (the formula for finding the total resistance when n identical resistors are connected in parallel).

9 r string = nr (the formula for finding the total resistance when n of the same resistor in series).

10 u1:u2=r1:r2 (the relationship between voltage and resistance in a series circuit: the ratio of voltage is equal to the ratio of resistance to which they correspond).

11 i1:i2=r2:r1 (the relationship between current and resistance in parallel circuits: the ratio of current is equal to the inverse ratio of the resistance to which they correspond).

2. Electric power part.

12 p=ui (empirical, suitable for any circuit).

13 p=w t (defined, suitable for any circuit).

14 q=i2rt (Joule's law, suitable for any circuit).

15．p=p1+p2+…+PN (suitable for any circuit).

16 W=UIT (empirical, suitable for any circuit).

17.p=i2r (composite formula, only suitable for purely resistive circuits).

18.p=u2 r (composite formula, only suitable for purely resistive circuits).

19.w=q (empirical, only suitable for purely resistive circuits.) where w is the work done by the current flowing through the conductor and q is the heat produced by the current flowing through the conductor).

20.w=i2rt (composite formula, only suitable for purely resistive circuits).

21.w=u2t r (composite formula, suitable only for purely resistive circuits).

22 p1:p2=u1:u2=r1:r2 (the relationship between electrical power and voltage and resistance in a series circuit: in a series circuit, the ratio of electrical power is equal to the ratio of voltage and resistance corresponding to them).

23 p1:p2=i1:i2=r2:r1 (the relationship between electrical power and current and resistance in parallel circuits: in parallel circuits, the ratio of electrical power is equal to the ratio of the current corresponding to them and equal to the inverse ratio of their corresponding resistance).