Calculating Total Current in Parallel Circuit
To solve this question, we need to understand Ohm's Law and how parallel circuits work. Ohm's Law states that V = IR, where V is voltage, I is current, and R is resistance.
In a parallel circuit, the voltage across each resistor is the same, and the total current supplied by the battery is the sum of the currents through each resistor.
The given circuit has a 10V battery and two resistors of 2Ω and 4Ω in parallel. The voltage across both resistors is 10V since they're in parallel.
We can calculate the current through each resistor using Ohm's Law:
For the 2Ω resistor:
\[ I_1 = \frac{V}{R_1} = \frac{10V}{2Ω} = 5A \]
For the 4Ω resistor:
\[ I_2 = \frac{V}{R_2} = \frac{10V}{4Ω} = 2.5A \]
Now, to calculate the total current delivered by the battery, we simply add the current through each resistor:
\[ I_{total} = I_1 + I_2 = 5A + 2.5A = 7.5A \]
So, the current delivered by the battery is 7.5A, with 5A going through the 2Ω resistor and 2.5A going through the 4Ω resistor.
