Answer :
Let's solve the problem step-by-step:
### a) List all givens
- Voltage (V) across the series circuit: 36 V
- Resistance of resistor 1: R₁ = 30 Ω
- Resistance of resistor 2: R₂ = 6 Ω
- Resistance of resistor 3: R₃ = 90 Ω
### b) List the unknown
The unknown is the current (I) flowing through the circuit.
### c) Show the formula
Ohm’s Law is used to relate voltage (V), current (I), and resistance (R). The formula is:
[tex]\[ V = I \times R \][/tex]
In a series circuit, the total resistance [tex]\( R_{\text{total}} \)[/tex] is the sum of the individual resistances:
[tex]\[ R_{\text{total}} = R₁ + R₂ + R₃ \][/tex]
To find the current (I), rearrange Ohm's Law to:
[tex]\[ I = \frac{V}{R_{\text{total}}} \][/tex]
### d) Substitute the givens and solve the equation
1. Calculate the total resistance:
[tex]\[ R_{\text{total}} = R₁ + R₂ + R₃ \][/tex]
[tex]\[ R_{\text{total}} = 30 Ω + 6 Ω + 90 Ω \][/tex]
[tex]\[ R_{\text{total}} = 126 Ω \][/tex]
2. Calculate the current using Ohm's Law:
[tex]\[ I = \frac{V}{R_{\text{total}}} \][/tex]
[tex]\[ I = \frac{36 \text{ V}}{126 \text{ Ω}} \][/tex]
[tex]\[ I = 0.286 \text{ A} \][/tex]
### e) List the answer with correct units
The current flowing through the series circuit is 0.286 A (amperes).
### a) List all givens
- Voltage (V) across the series circuit: 36 V
- Resistance of resistor 1: R₁ = 30 Ω
- Resistance of resistor 2: R₂ = 6 Ω
- Resistance of resistor 3: R₃ = 90 Ω
### b) List the unknown
The unknown is the current (I) flowing through the circuit.
### c) Show the formula
Ohm’s Law is used to relate voltage (V), current (I), and resistance (R). The formula is:
[tex]\[ V = I \times R \][/tex]
In a series circuit, the total resistance [tex]\( R_{\text{total}} \)[/tex] is the sum of the individual resistances:
[tex]\[ R_{\text{total}} = R₁ + R₂ + R₃ \][/tex]
To find the current (I), rearrange Ohm's Law to:
[tex]\[ I = \frac{V}{R_{\text{total}}} \][/tex]
### d) Substitute the givens and solve the equation
1. Calculate the total resistance:
[tex]\[ R_{\text{total}} = R₁ + R₂ + R₃ \][/tex]
[tex]\[ R_{\text{total}} = 30 Ω + 6 Ω + 90 Ω \][/tex]
[tex]\[ R_{\text{total}} = 126 Ω \][/tex]
2. Calculate the current using Ohm's Law:
[tex]\[ I = \frac{V}{R_{\text{total}}} \][/tex]
[tex]\[ I = \frac{36 \text{ V}}{126 \text{ Ω}} \][/tex]
[tex]\[ I = 0.286 \text{ A} \][/tex]
### e) List the answer with correct units
The current flowing through the series circuit is 0.286 A (amperes).
