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Answer :
Sure, let's solve the problem step-by-step:
1. Identify the Components:
- You have a battery with a voltage of 12 volts (V).
- There is a [tex]$4 \Omega$[/tex] resistor and a [tex]$6 \Omega$[/tex] resistor connected in series.
2. Calculate the Total Resistance:
- In a series circuit, the total resistance is the sum of the individual resistances.
- Total Resistance = Resistance of the first resistor + Resistance of the second resistor
- Total Resistance = 4 Ω + 6 Ω = 10 Ω
3. Calculate the Current Using Ohm's Law:
- Ohm's Law states: [tex]\( I = \frac{V}{R} \)[/tex], where [tex]\( I \)[/tex] is the current, [tex]\( V \)[/tex] is the voltage, and [tex]\( R \)[/tex] is the resistance.
- Here, [tex]\( V = 12 \text{ volts} \)[/tex] and [tex]\( R = 10 \text{ ohms} \)[/tex].
- Current, [tex]\( I = \frac{12}{10} = 1.2 \text{ amperes (A)} \)[/tex].
4. Calculate the Voltage Drop Across Each Resistor:
- The voltage drop across a resistor in a series circuit can be calculated using Ohm's Law: [tex]\( V = IR \)[/tex].
- Voltage drop across the 4 Ω resistor:
- [tex]\( V = 1.2 \text{ A} \times 4 \text{ Ω} = 4.8 \text{ volts} \)[/tex]
- Voltage drop across the 6 Ω resistor:
- [tex]\( V = 1.2 \text{ A} \times 6 \text{ Ω} = 7.2 \text{ volts} \)[/tex]
In conclusion, the total resistance is 10 Ω, the current flowing through the circuit is 1.2 A, the voltage drop across the 4 Ω resistor is 4.8 volts, and the voltage drop across the 6 Ω resistor is 7.2 volts.
1. Identify the Components:
- You have a battery with a voltage of 12 volts (V).
- There is a [tex]$4 \Omega$[/tex] resistor and a [tex]$6 \Omega$[/tex] resistor connected in series.
2. Calculate the Total Resistance:
- In a series circuit, the total resistance is the sum of the individual resistances.
- Total Resistance = Resistance of the first resistor + Resistance of the second resistor
- Total Resistance = 4 Ω + 6 Ω = 10 Ω
3. Calculate the Current Using Ohm's Law:
- Ohm's Law states: [tex]\( I = \frac{V}{R} \)[/tex], where [tex]\( I \)[/tex] is the current, [tex]\( V \)[/tex] is the voltage, and [tex]\( R \)[/tex] is the resistance.
- Here, [tex]\( V = 12 \text{ volts} \)[/tex] and [tex]\( R = 10 \text{ ohms} \)[/tex].
- Current, [tex]\( I = \frac{12}{10} = 1.2 \text{ amperes (A)} \)[/tex].
4. Calculate the Voltage Drop Across Each Resistor:
- The voltage drop across a resistor in a series circuit can be calculated using Ohm's Law: [tex]\( V = IR \)[/tex].
- Voltage drop across the 4 Ω resistor:
- [tex]\( V = 1.2 \text{ A} \times 4 \text{ Ω} = 4.8 \text{ volts} \)[/tex]
- Voltage drop across the 6 Ω resistor:
- [tex]\( V = 1.2 \text{ A} \times 6 \text{ Ω} = 7.2 \text{ volts} \)[/tex]
In conclusion, the total resistance is 10 Ω, the current flowing through the circuit is 1.2 A, the voltage drop across the 4 Ω resistor is 4.8 volts, and the voltage drop across the 6 Ω resistor is 7.2 volts.
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