# Electric Circuits

Computer Science I · Physics · https://tryals.app/learn/computer-science-i/electric-circuits

A **circuit** is a closed loop where charge flows. Three core quantities describe any circuit:

- **Current** $I$: rate of charge flow in **amperes** ($C/s$). Conventional current moves from high to low potential.
- **Voltage** $V$: potential difference driving current, measured in **volts**.
- **Resistance** $R$: opposition to current flow, measured in **ohms**.

These are tied by **Ohm's law**: $V = I R$. Rearranged as $I = V/R$, current equals voltage divided by resistance. The **power** dissipated as heat is $P = IV = I^2 R$, which is why active electronics get hot.

## Combining Components

Components wire in two basic ways:

| Connection | Rule | Total Resistance |
| --- | --- | --- |
| **Series** | Same current | Add ($R = R_1 + R_2$) |
| **Parallel** | Same voltage | Inverse/split |

For two parallel branches, $R = \frac{R_1 R_2}{R_1 + R_2}$. Adding parallel paths **decreases** total resistance.

> **Common Pitfall:** Swapping rules. In **series**, resistances **add** (total goes up). In **parallel**, total resistance is **smaller** than the smallest branch. Also remember $I = V/R$: more resistance means **less** current.

## Practice questions

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

### 1. A 24 volt supply is connected across a 6 ohm resistor. What current flows, in amperes?

**Answer:** 4

**Why:** Ohm's law gives I = V/R = 24/6 = 4 amperes.

The relationship is worth reading as a statement about what each quantity does: voltage is the push, resistance is the opposition, and current is what results. Doubling the voltage doubles the current; doubling the resistance halves it.

The power dissipated follows as P = VI = 24 x 4 = 96 watts, all of it becoming heat in the resistor - which is why resistors have power ratings and why a component rated for a quarter of a watt fails immediately in a circuit like this one.

Page: https://tryals.app/practice/computer-science-i/electric-circuits/a-24-volt-supply-is-connected-across-a-6-ohm-resistor-what-current

### 2. Three resistors of 2, 3 and 7 ohms are connected in series across a 24 volt supply. What current flows, in amperes?

**Answer:** 2

**Why:** 2 + 3 + 7 = 12 ohms, and 24/12 = 2 A. The same current passes through all three because there is only one path, which is exactly what defines a series connection.

Page: https://tryals.app/practice/computer-science-i/electric-circuits/three-resistors-of-2-3-and-7-ohms-are-connected-in-series-across-a

### 3. A 6 ohm resistor and a 3 ohm resistor are connected in parallel. What is their combined resistance, in ohms?

**Answer:** 2

**Why:** 18/9 = 2 ohms. The result is smaller than either branch, which is the signature of a parallel connection: adding another path always gives the current somewhere else to go, so the total resistance drops.

Page: https://tryals.app/practice/computer-science-i/electric-circuits/a-6-ohm-resistor-and-a-3-ohm-resistor-are-connected-in-parallel-what

### 4. Adding a resistor in series increases total resistance; adding one in parallel decreases it. Why does adding a component ever make a circuit conduct more easily?

A. Because parallel resistors have negative resistance, which subtracts from the total.
B. Because a parallel resistor cancels part of the field produced by the first.
C. Because current in parallel circuits flows faster, reducing the effective resistance.
D. Because a parallel resistor adds another route for current.

**Answer:** D. Because a parallel resistor adds another route for current.

**Why:** The pipe analogy is exact enough to be useful: two in series make one longer obstructed route, and two in parallel give the water two routes, so more flows for the same pressure. Series resistances add and parallel *conductances* add. It is why household wiring is parallel, every appliance gets full voltage and switches independently, and why adding appliances is what a breaker watches for.

Page: https://tryals.app/practice/computer-science-i/electric-circuits/adding-a-resistor-in-series-increases-total-resistance-adding-one-in

### 5. A CPU's power consumption rises roughly with frequency times voltage squared, and higher clocks need higher voltage. What did that relationship do to processor design around 2005?

A. Made transistors stop shrinking, ending Moore's law entirely
B. Ended clock scaling, since power grew faster than performance
C. Forced a switch from silicon to alternative semiconductors
D. Required liquid cooling in all consumer processors

**Answer:** B. Ended clock scaling, since power grew faster than performance

**Why:** Power roughly cubed with clock speed once the voltage increase is included, so the heat wall arrived while transistor counts kept climbing. The budget went sideways into cores, which turned a hardware limit into a software problem, since a sequential program stopped getting faster by waiting.

Page: https://tryals.app/practice/computer-science-i/electric-circuits/a-cpus-power-consumption-rises-roughly-with-frequency-times-voltage

### 6. Select every statement that is TRUE of resistors in circuits.

A. In series the resistances add
B. Components in parallel have the same voltage across them
C. Components in series carry the same current
D. Two resistors in parallel have a total resistance larger than either one
E. Power dissipated in a resistor is the current squared times the resistance

**Answer:** A. In series the resistances add; B. Components in parallel have the same voltage across them; C. Components in series carry the same current; E. Power dissipated in a resistor is the current squared times the resistance

**Why:** The 6 and 3 ohm pair combined to 2 ohms, smaller than both, so option three is false. The rest are exactly as taught: series shares current and adds resistance, parallel shares voltage, and power grows with the square of the current.

Page: https://tryals.app/practice/computer-science-i/electric-circuits/select-every-statement-that-is-true-of-resistors-in-circuits

### 7. Complete Ohm's law rearranged for the current.

**Answer:** For a component of resistance R across a voltage V, the current is **V divided by R**.

**Why:** Dividing V equals I times R by R isolates the current as V over R. Checking the behaviour at the extremes settles it: an enormous resistance should give almost no current, which only the division delivers.

Page: https://tryals.app/practice/computer-science-i/electric-circuits/complete-ohms-law-rearranged-for-the-current