A circuit connected to a 12V battery has three 50 Ohm resistors with two connected in series, and parallel to the third. Calculate the total resistance and current.

Total resistance=33.3 ohms

Current=0.36 amperes

Explanation:

Voltage=12v

R1=50 ohms

R2=50 ohms

R3=50 ohms

Two connected in series:

R1+R2=50+50=100 ohms

In parallel

1/R=1/50 + 1/100

1/R=(2+1)/100

1/R=3/100

Cross multiplying we get

100=3R

Divide both sides by3

100/3=3R/3

33.3=R

Total resistance=33.3 ohms

Current=voltage ➗ resistance

Current=12 ➗ 33.3

Current=0.36 amperes

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