Final answer:
The total current flowing through the system with two parallel resistors of 2Ω and 5Ω connected to a 10V battery is approximately 7 Amps.
Step-by-step explanation:
The question is asking for the total current flowing through a system with two resistors in parallel, with resistances of 2Ω and 5Ω, when connected to a 10V battery. When resistors are in parallel, the total current through the system is the sum of the individual currents through each resistor. The individual resistances can be used to find the current through each branch using Ohm’s Law (I = V/R).
First, we determine the equivalent resistance (Req) of the parallel resistors using the formula: 1/Req = 1/R1 + 1/R2. Plugging in our values gives us 1/Req = 1/2Ω + 1/5Ω, which simplifies to Req ≈ 1.43Ω (rounded to two decimal places).
Next, using the equivalent resistance and the voltage of the battery, we calculate the total current (Itotal) that flows through the system: Itotal = V / Req. We have Itotal ≈ 10V / 1.43Ω, which gives us ≈ 6.99A. So, roughly 7A flows through the circuit.
Therefore, the total current flowing through the system is approximately 7 Amps.