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Calculate Current I₁ in 6V Series Circuit with 3Ω and 2Ω Resistors
Physics
Grade 10 of Junior High School
Question Content
Find the labelled current I₁ in the series circuit with a 6V power supply, a 3Ω resistor, and a 2Ω resistor.
Correct Answer
1.2 A
Detailed Solution Steps
1
Step 1: Identify the circuit type. The two resistors (3Ω and 2Ω) are connected in series, so the total resistance of the circuit is the sum of individual resistances: R_total = 3Ω + 2Ω = 5Ω.
2
Step 2: Apply Ohm's Law (V = IR), where V is the voltage of the power supply, I is the total current in the circuit, and R is the total resistance. Rearrange the formula to solve for current: I = V/R_total.
3
Step 3: Substitute the known values into the formula: I₁ = 6V / 5Ω = 1.2 A. Since this is a series circuit, the current I₁ is the same throughout the circuit.
Knowledge Points Involved
1
Series Circuit Resistance
In a series circuit, resistors are connected end-to-end, so the total resistance is the arithmetic sum of all individual resistances (R_total = R₁ + R₂ + ... + Rₙ). This is because the current must pass through each resistor sequentially, so each resistor adds to the total opposition to current flow.
2
Ohm's Law
Ohm's Law states the relationship between voltage (V), current (I), and resistance (R) in an electrical circuit, expressed as V = IR. It can be rearranged to solve for any unknown variable: I = V/R or R = V/I. This law applies to all ohmic resistors (resistors that maintain a constant resistance with changing voltage/current) in direct current circuits.
3
Current in Series Circuits
In a series circuit, there is only one path for electric current to flow, so the magnitude of the current is identical at every point in the circuit. The same amount of charge passes through each component per unit time.
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