Question

Draw a circuit with a 12-volt battery, a 100 ohms resistor in series, and two resistors (each of value 200 ohms) in parallel. What is the total resistance of the circuit?

Answer 1

Answer:

200 Ω

Explanation:

Hi there!

Please see below for the circuit diagram.

1) Find the total resistance of the resistors in parallel

Total resistance in parallel equation: $\frac{1}{R_T} = \frac{1}{R_1} +\frac{1}{R_2}$

Both the resistors measure 200 Ω. Plug these into the equation as R₁ and R₂:

$\frac{1}{R_T} = \frac{1}{200} +\frac{1}{200}\\\frac{1}{R_T} = \frac{1}{100}\\R_T=100$

Therefore, the total resistance of the resistors in parallel is 100 Ω.

2) Find the total resistance of the circuit

Now, to find the total resistance of the circuit, we must add the 100 Ω we just solved for and the 100 Ω for the other resistor placed in series:

100 Ω + 100 Ω = 200 Ω

Therefore, the total resistance of the circuit is 200 Ω.

I hope this helps!