# Current, Resistance, and DC Circuits

Physics I · Principles of Electromagnetism and Optics · https://tryals.app/learn/physics-i/current-resistance-and-dc-circuits

## Electric Current & Ohm's Law

A wire carries no extra net charge when current flows; electrons drift slowly at about 0.1 mm/s. A bulb lights instantly because the electric push travels near light speed, like water through a hose.

**Electric current** is the rate of charge flow: $I = \frac{dQ}{dt}$, unit: ampere (A).

**Ohm's law** links voltage, current, and resistance: $V = IR$.

**Resistivity** governs material geometry: $R = \rho \frac{L}{A}$, where $\rho$ is material resistivity, $L$ is length, and $A$ is cross-sectional area.

**Power dissipated** in a resistor is given by: $P = IV = I^2R = \frac{V^2}{R}$.

## Circuits, Power & Pitfalls

**Joule heating** turns electrical energy into heat: $E = Pt = I^2Rt$. This is why power lines use high voltage and low current to minimize losses.

| Configuration | Equivalent $R$ |
| --- | --- |
| Series | $R_{\text{eq}} = R_1 + R_2 + \dots$ |
| Parallel | $\frac{1}{R_{\text{eq}}} = \frac{1}{R_1} + \frac{1}{R_2} + \dots$ |

> **Key insight:** Series resistors share identical current, while parallel resistors share identical voltage.

> **Common pitfall:** Current is never "used up" in a circuit. The exact same current returns to the battery; what gets consumed is **energy per charge** (voltage).

## Practice questions

5 of this lesson's 13 practice questions, with answers. The full set is in the app.

### 1. Which formulas give the power dissipated in a resistor?

A. $P = I^{2}R$
B. $P = IR^{2}$
C. $P = V^{2}/R$
D. $P = IV$

**Answer:** A. $P = I^{2}R$; C. $P = V^{2}/R$; D. $P = IV$

**Why:** All three are equivalent via $V = IR$; $P =  IR^{2}$ has the wrong exponent.

Page: https://tryals.app/practice/physics-i/current-resistance-and-dc-circuits/which-formulas-give-the-power-dissipated-in-a-resistor

### 2. Complete the following passage by choosing the correct terms from the word bank.

**Answer:** Resistors in **series** share the same current, while resistors in **parallel** share the same voltage.

**Why:** Series: same I, voltages add. Parallel: same V, currents add.

Page: https://tryals.app/practice/physics-i/current-resistance-and-dc-circuits/complete-the-following-passage-by-choosing-the-correct-terms-from-the

### 3. Sort each component by its behavior in a DC circuit.

**Answer:**

- Stores energy: Capacitor, Inductor, Battery (ideal)
- Dissipates energy: Resistor, Light bulb, Heating coil

**Why:** Capacitors and inductors store energy; resistors and bulbs dissipate it as heat/light.

Page: https://tryals.app/practice/physics-i/current-resistance-and-dc-circuits/sort-each-component-by-its-behavior-in-a-dc-circuit

### 4. Two bulbs: a 60 W and a 100 W (both rated for mains voltage). You connect them **in series** across the mains. Which bulb glows brighter?

A. They glow equally: same current through both
B. Neither lights: series bulbs cancel
C. The 60 W bulb: larger resistance, shared current
D. The 100 W bulb, as its rating promises

**Answer:** C. The 60 W bulb: larger resistance, shared current

**Why:** The 60 W bulb has the larger filament resistance ($R = V^{2}/P$). In series, both carry the same current, and $P = I^{2}R$ favours the larger $R$, so the "weaker" bulb wins. Power ratings only apply in the circuit they were rated for.

Page: https://tryals.app/practice/physics-i/current-resistance-and-dc-circuits/two-bulbs-a-60-w-and-a-100-w-both-rated-for-mains-voltage-you

### 5. Adding a resistor in parallel DECREASES total resistance while adding one in series increases it. Why do the two arrangements differ in sign?

A. Because the formula for parallel resistance involves reciprocals
B. Because voltage divides in parallel and current divides in series
C. Because a parallel branch opens an additional path for current
D. Because parallel resistors share the current and so heat up less

**Answer:** C. Because a parallel branch opens an additional path for current

**Why:** More paths means more total current for the same voltage, and resistance is voltage over current. The reciprocal formula is the consequence, not the reason.

Page: https://tryals.app/practice/physics-i/current-resistance-and-dc-circuits/adding-a-resistor-in-parallel-decreases-total-resistance-while-adding