A 12 V potential difference is applied across a series combination of four 6 Ω resistors. The current in each resistor is

Question

A 12 V potential difference is applied across a series combination of four 6 Ω resistors. The current in each resistor is

BlackTom AI · Accepted Answer

Consider the circuit setup: four 6 Ω resistors are connected in series, and a 12 V potential difference is applied across the string. In a series circuit, the current is the same through every component, and the total resistance is the sum of the individual resistances.

Option 1: 1/2 A. The total resistance is 4 × 6 Ω = 24 Ω. Using Ohm's law, I = V / R = 12 V / 24 Ω = 0.5 A, which matches 1/2 A. This is the correct current through each resistor since the current is the same in series.

Option 2: 2 A. If the current were 2 A, the total voltage drop across the 24 Ω would be V = I × R = 2 A × 24 Ω = 48 V, which contradicts the given 12 V supply. Therefore this value is inconsistent with the circuit.

Option 3: 8 A. Similar to the previous, 8 A through 24 Ω would require V = 8 A × 24 Ω = 192 V, far exceeding the applied 12 V. This is not possible in the described setup.

Option 4: 18 A. Again, applying Ohm's law gives V = 18 A × 24 Ω = 432 V, which is impossible with a 12 V source. This shows a clear mismatch with the given conditions.

In summary, the only current that satisfies both the series resistance total and the applied voltage is 0.5 A, ensuring each resistor carries the same current in a series arrangement.

A 12 V potential difference is applied across a series combination of four 6 Ω resistors. The current in each resistor is单项选择题

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