Section 9.4: Current and Resistance
Electric current is the rate of flow of electric charge. Resistance is the property of a material that resists the flow of current.
\[
I = \frac{Q}{t}
\]
where:
\( I \) = current (A, amperes)
\( Q \) = charge (C, coulombs)
\( t \) = time (s)
\( I \) = current (A, amperes)
\( Q \) = charge (C, coulombs)
\( t \) = time (s)
\[
R = \frac{V}{I}
\]
where:
\( R \) = resistance (Ω)
\( V \) = potential difference (V)
\( I \) = current (A)
\( R \) = resistance (Ω)
\( V \) = potential difference (V)
\( I \) = current (A)
Ohm's Law states that the current through a conductor is directly proportional to the voltage across it, provided the temperature remains constant.
Example 1: Current in a Circuit
A charge of 20 C passes through a wire in 4 s. Find the current.
\( I = Q/t = 20 / 4 = 5 \, \text{A} \)
Example 2: Resistance of a Resistor
A resistor has a voltage of 12 V across it and a current of 3 A flows. Find its resistance.
\( R = V/I = 12 / 3 = 4 \, \Omega \)
Practice Problems
- A current of 2 A flows for 10 s. Calculate the charge transported.
- A resistor of 8 Ω has a current of 0.5 A. Find the voltage across it.
- If 10 C flows in 2 s through a wire, what is the current?
- A 6 V battery is connected across a resistor, producing a current of 0.2 A. Find the resistance.
- A conductor has a resistance of 12 Ω. If 24 V is applied, calculate the current.