Lecture 05

Serial and parallel connection of voltage source and current source

Serial and parallel connection of voltage source and current source

​

• serial connection of ideal voltage sources

​

(KVL) u = u_S1 + u_S2 ... + u_Sn

Note:

• u_Si takes reference direction, and each might not be

consistent with each other.

equivalent circuit

Serial and parallel connection of voltage source and current source

​

• parallel connection of ideal voltage sources

​

(KVL) u = u_S1 = u_S2 ... = u_Sn

Note: Only the voltage sources with the same value can be connected in parallel. The current is not determined because it depends on external circuit.

Output voltage remains the same,

then why bother to connect the voltage sources?

The current of each voltage source can be different, and

the parallel connection can increase the output power.

equivalent circuit

Serial and parallel connection of voltage source and current source

​

• serial connection of ideal voltage sources with the other branches (components) in the circuit.

​

(KVL+VCL)

u = u_S1 + i*R₁ +...+ u_Sn + i*R_n =

(u_S1 + u_Sn)+(i*R₁ + i*R_n)= u_S + i*R

R₁

R_n

i

R

u_S

i

+

-

equivalent circuit

Serial and parallel connection of voltage source and current source

​

• parallel connection of ideal voltage sources with the other branches (components) in the circuit.

​

+

+

-

-

u_S1

u

component

Including resistor, voltage source, current source,

dependent current source, but not dependent voltage

source.

R

+

-

u_S1

+

-

u

equivalent circuit

Serial and parallel connection of voltage source and current source

​

• parallel connection of ideal current sources

​

(KCL) i = i_S1 + i_S2 ... + i_Sn

Note:

• i_Si takes reference direction, and each might not be

consistent with each other.

equivalent circuit

Serial and parallel connection of voltage source and current source

​

• serial connection of ideal current sources

​

equivalent circuit

(KCL) i = i_S1 = i_S2 ... = i_Sn

Note: Only the current sources with the same value can be connected in series. The voltage is not determined because it depends on external circuit.

Serial and parallel connection of voltage source and current source

​

• parallel connection of ideal current sources with the other branches (components) in the circuit.

​

(KCL+VCL)

i = i_n -u/R_n = (i_(n-1)+i_sn) - u/R_n = (i_s1 +i_s2 +...+i_sn)- (u/R₁+ ...+u/R_n)

= i_s – u/R

​

i_s = i_s1 +i_s2 +...+i_sn; 1/R = 1/R₁+ ...+1/R_n

equivalent circuit

R

Series and parallel connection of voltage source and current source

​

• serial connection of ideal current sources with the other branches (components) in the circuit.

​

component

Including resistor, voltage source, current source,

dependent voltage source, but not dependent current

source.

equivalent circuit