Problem: Find the current through the 6 Ω resistor in the circuit where a 12 V battery is connected to a 4 Ω resistor in series with a parallel combination of a 6 Ω resistor and a 12 Ω resistor.
Steps
- Simplify the parallel resistors: The 6 Ω and 12 Ω resistors are in parallel. For two resistors in parallel, their equivalent resistance is found using
so . This works because parallel branches share the same voltage, so their equivalent resistance combines inversely.
- Find the total circuit resistance: This parallel equivalent is in series with the 4 Ω resistor, so
Series resistances add directly because the same current flows through both.
- Find the total current from the battery: Using Ohm's law ,
This is the current that flows through the 4 Ω resistor before splitting between the two parallel branches.
- Find the voltage across the parallel combination: The voltage drop across the 4 Ω series resistor is
The remaining voltage appears across the parallel pair: This 6 V is the voltage across both the 6 Ω and 12 Ω resistors, since parallel branches share the same voltage.
- Find the current through the 6 Ω resistor: Apply Ohm's law to just the 6 Ω resistor:
Answer: The current through the 6 Ω resistor is .
