Questions: Series or Parallel Circuit? 2. In the circuit diagram below, the battery has an EMF of 3 V and all the resistors have a resistance of 2 Ω. a. How are they connected (series, parallel, or neither)? Redraw the circuit below to make the connections clearer. b. What is the total resistance of the circuit? c. What is the current put out by the battery? d. What is the power put out by the battery?

Solution Steps

The circuit consists of multiple resistors connected in a combination of series and parallel. To simplify, redraw the circuit to make the connections clearer.

Redrawing the circuit, we see that the resistors are connected in a parallel configuration. Each branch has a resistor of 2 Ω.

For resistors in parallel, the total resistance \( R_{total} \) is given by: \[ \frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \frac{1}{R_4} \] Since all resistors \( R_1, R_2, R_3, R_4 \) are 2 Ω: \[ \frac{1}{R_{total}} = \frac{1}{2} + \frac{1}{2} + \frac{1}{2} + \frac{1}{2} = 2 \] \[ R_{total} = \frac{1}{2} = 0.5 \, \Omega \]

Final Answer