## Adding Signed Numbers In electrical systems, you often encounter **positive and negative values** that must be added together. This happens with: - Voltage rise and drop calculations - Net current flows - Temperature changes - Phase shifts Understanding how to add signed numbers is essential for solving these problems accurately. ### Case 1: Adding Two Numbers with the Same Sign When both numbers have the **same sign**, you: - **Add their absolute values** - **Keep the common sign** #### Example 1 $+3 + (+5) = +8$ #### Example 2 $-4 + (-7) = -11$ **Application:** If two components each produce a −2.5 V drop across a circuit, the total voltage drop is: $ -2.5 + (-2.5) = -5.0 \ \text{V} $ ### Case 2: Adding Numbers with Different Signs When the signs are **different**, you: - **Subtract the smaller absolute value from the larger one** - **Take the sign of the number with the larger absolute value** #### Example 1 $+7 + (-4)$ → $7 - 4 = 3$, and 7 is positive → **Answer: +3** #### Example 2 $-9 + (+5)$ → $9 - 5 = 4$, and 9 is negative → **Answer: -4** ### Using a Number Line (Optional Visual Tool) You can use a number line to visualize these operations: - Start at the first number - Move **right** for adding a positive - Move **left** for adding a negative Example: Start at $+6$, then add $-3$ → move 3 units left → land at $+3$ ## Real-World Electrical Example You have a battery bank with a voltage gain of +24 V, but a voltage drop of −6 V across a connected load. The net voltage is: $ +24 + (-6) = +18 \ \text{V} $ In a circuit like this, you add signed values to find the effective voltage or current. ## Practice Try these by hand or on a number line: 1. $+12 + (-5) = \ ?$ 2. $-4 + (-8) = \ ?$ 3. $-10 + (+15) = \ ?$ 4. $+6 + (-6) = \ ?$ ## Summary - **Same signs** → add values, keep the sign - **Different signs** → subtract absolute values, use sign of the larger number - Adding signed numbers is used in **voltage calculations**, **net current**, and **temperature changes**