In a simple circuit with a fixed applied voltage $V$, how does increasing the resistance $R$ affect the electric current $I$ according to Ohm’s law?

• A. The current stays the same because current is independent of resistance when voltage is fixed.
• B. The current decreases because $I=\frac{V}{R}$, so increasing $R$ makes $I$ smaller.
• C. The current becomes zero for any increase in $R$, because any resistance blocks all current.
• D. The current increases because $I=\frac{R}{V}$, so increasing $R$ makes $I$ larger.

Answer: (B)

Verified step by step guidance

1. Recall Ohm's law, which relates voltage (V), current (I), and resistance (R) in a simple circuit: \(I = \frac{V}{R}\).
2. Understand that in this formula, voltage (V) is fixed, meaning it does not change as resistance changes.
3. Analyze how current (I) depends on resistance (R): since current is voltage divided by resistance, increasing resistance will affect the current inversely.
4. Conclude that as resistance (R) increases, the denominator in the fraction \(\frac{V}{R}\) becomes larger, which makes the overall value of current (I) smaller.
5. Therefore, increasing resistance in a circuit with fixed voltage causes the electric current to decrease, but it does not necessarily become zero unless resistance is infinitely large.