1. What is the relationship between the current through each resistor and the current through the battery?

2. What is the relationship between the voltage across the battery and the voltage across each resistor?

simple circuit, short answers are fine, thanks.

1.Components in a series circuit share the same current.

2.The sum of individual voltage drop in a series circuit equals that supply voltage.

Explanation:

In a simple circuit, the amount of current is the same flowing through the resistor and the battery as long as it is a series circuit.Components in a series circuit share the same current.

In a series circuit, the total resistance equals the sum of individual resistance

The sum of individual voltage drop in a series circuit equals that supply voltage.

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west