# Find currents using KVL

Find resistor currents using KVL.

Solution:

$R_1$ and $V_1$ are parallel. So the voltage across $R_1$ is equal to $V_1$. This can be also calculated using KVL in the left hand side loop:

# Problem 2-1: Linearity of Functions

Which one(s) of the following functions is linear?

a) $y=x+1$.
b) $y=2x+1$.
c) $y=1$.
d) $y=x^2+x+1$.
e) $y=x^1+1$.
f) $y=\frac{1}{x}$.
g) $y=\sin(x)$.

h) $y=\sqrt{x}$.
i) $y=x+\frac{1}{1-x}$.

j) $5x+2y-1=0$.
k) $y=x+c^2$. ($c$ is an arbitrary constant).

Solution
a) Linear
b) Linear
c) Linear
d) Nonlinear
e) Linear
f) Nonlinear

g) Nonlinear
h) Nonlinear
i) Nonlinear
j) Linear

k) Linear