Let's solve the problem step by step.
Given Circuit:
- A series circuit with a 9 V battery and three resistors:
- R₁ = 3 Ω
- R₂ = 10 Ω
- R₃ = 5 Ω
All resistors are connected in
series, meaning the same current flows through each component.
---
Step 1: Find Total Resistance (R_total)
In a series circuit, total resistance is the sum of individual resistances:
\[
R_{\text{total}} = R_1 + R_2 + R_3 = 3\,\Omega + 10\,\Omega + 5\,\Omega = 18\,\Omega
\]
---
Step 2: Use Ohm’s Law to Find Current (I)
Ohm’s Law:
\[
V = I \cdot R \quad \Rightarrow \quad I = \frac{V}{R}
\]
\[
I = \frac{9\,\text{V}}{18\,\Omega} = 0.5\,\text{A}
\]
So, the current flowing through the circuit is
0.5 A.
---
Step 3: Find Voltage Across Each Resistor
Using Ohm’s Law again: \( V = I \cdot R \)
- Voltage across R₁:
\[
V_1 = I \cdot R_1 = 0.5\,\text{A} \cdot 3\,\Omega = 1.5\,\text{V}
\]
- Voltage across R₂:
\[
V_2 = I \cdot R_2 = 0.5\,\text{A} \cdot 10\,\Omega = 5\,\text{V}
\]
- Voltage across R₃:
\[
V_3 = I \cdot R_3 = 0.5\,\text{A} \cdot 5\,\Omega = 2.5\,\text{V}
\]
Check: Total voltage = \(1.5 + 5 + 2.5 = 9\,\text{V}\)
✔
---
Summary of Results:
-
Total Resistance: 18 Ω
-
Current (I): 0.5 A
-
Voltage across R₁ (3 Ω): 1.5 V
-
Voltage across R₂ (10 Ω): 5 V
-
Voltage across R₃ (5 Ω): 2.5 V
---
Answer:
The current in the circuit is
0.5 A, and the voltages across the resistors are:
- R₁: 1.5 V
- R₂: 5 V
- R₃: 2.5 V
This satisfies Kirchhoff's Voltage Law (sum of voltages equals source voltage).
Parent Tip: Review the logic above to help your child master the concept of series circuit math.
