Suppose you have the following circuit. Resistors are labeled 1 through 4 and nodes in the circuit are labeled A, B, and C for convenience of reference. You know that the circuit contains a 12-Volt battery, $I_1 = 50 \text{ mA}$, $R_1=80 \Omega$, $R_3=300 \Omega$, $R_4=500 \Omega$, and $\Delta V_4=5 \text{ V}$. What are the potential differences $\Delta V_1$, $\Delta V_2$, $\Delta V_3$, and the resistance $R_2$?

Circuit with Resistors in Series and Parallel

• $\Delta V_{\text{bat}} = 12\text{ V}$
• $I_1 = 50 \text{ mA}$
• $R_1=80 \Omega$
• $R_3=300 \Omega$
• $R_4=500 \Omega$
• $\Delta V_4=5 \text{ V}$

• $\Delta V_1$, $\Delta V_2$, $\Delta V_3$, $R_2$.

• The wire has very very small resistance when compared to the other resistors in the circuit: This allows there to be no energy loss across the wires and no potential difference across them either simplifying down the model.
• The circuit is in a steady state: It takes a finite amount of time for a circuit to reach steady state and set up a charge gradient. Making this assumption means the current is not changing with time in any branch of the circuit.
• Approximating the battery as a mechanical battery: This means the battery will supply a steady power source to the circuit to keep it in steady state.
• The resistors in the circuit are made of Ohmic materials: Ohmic materials have a linear relationship between voltage and current, this allows us to use ohms law.

• We represent Ohm's Law as

• We represent the equivalent resistance of multiple resistors arranged in series as

• We represent the equivalent resistance of mult