How do i find the equivalent voltage source?

[An1MuS]

Homework Statement

How do i find the equivalent voltage source of...

1) Two AC voltage sources in series with same frequency and phase = ?
2) One AC voltage source in series with a DC voltage source = ?

Homework Equations

Equation of a AC voltage source as a function of time $$V(t)=V_m * sin( \omega *t + \theta )$$

The Attempt at a Solution

1) $$V(t)=(V_{m_1}+V_{m_2}) * sin( \omega *t + \theta )$$
2) $$V(t)=(V_{DC}+V_m) * sin( \omega *t + \theta )$$

 

[gneill]

Homework Statement

How do i find the equivalent voltage source of...

1) Two AC voltage sources in series with same frequency and phase = ?
2) One AC voltage source in series with a DC voltage source = ?

Homework Equations

Equation of a AC voltage source as a function of time $$V(t)=V_m * sin( \omega *t + \theta )$$

The Attempt at a Solution

1) $$V(t)=(V_{m_1}+V_{m_2}) * sin( \omega *t + \theta )$$
2) $$V(t)=(V_{DC}+V_m) * sin( \omega *t + \theta )$$

Your first answer is correct. The second is not; a DC source is a constant value that does not vary sinusoidally. Suppose you had the two functions f(t) = 4 and g(t) = sin(ωt). What would be the result of adding them: f(t) + g(t) = ?

 

[An1MuS]

since f(t) = 4, then adding g(t) + f(t) would be the same as g(t) + 4...

Ah that makes sense, if i add a constant function such as DC current to some other non-constant like the sinusoidal function of AC current, it's like adding it's value, so the answer to b) is

$$V(t)=V_{DC}+V_m*sin(\omega *t + \theta)$$

 

[gneill]

since f(t) = 4, then adding g(t) + f(t) would be the same as g(t) + 4...

Ah that makes sense, if i add a constant function such as DC current to some other non-constant like the sinusoidal function of AC current, it's like adding it's value, so the answer to b) is

$$V(t)=V_{DC}+V_m*sin(\omega *t + \theta)$$

Much better!