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Answer :
To solve the question, we need to determine the total resistance, the current, and the voltage drop across each resistor in a series circuit. Let's go through the steps one by one:
1. Total Resistance:
In a series circuit, the total resistance is simply the sum of all the resistances.
- We have two resistors: a [tex]\(4 \Omega\)[/tex] resistor and a [tex]\(6 \Omega\)[/tex] resistor.
- Total resistance [tex]\(R_{total} = 4 \Omega + 6 \Omega = 10 \Omega\)[/tex].
2. Current in the Circuit:
We can calculate the current in the circuit using Ohm's Law, which 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.
- The total voltage from the battery is [tex]\(12 V\)[/tex].
- Using the total resistance, the current [tex]\(I = \frac{12 \, V}{10 \, \Omega} = 1.2 \, A\)[/tex].
3. Voltage Drop Across Each Resistor:
The voltage drop across a resistor in a series circuit can be found using Ohm's Law, [tex]\(V = I \times R\)[/tex].
- For the [tex]\(4 \Omega\)[/tex] resistor:
[tex]\[
\text{Voltage drop} = 1.2 \, A \times 4 \, \Omega = 4.8 \, V
\][/tex]
- For the [tex]\(6 \Omega\)[/tex] resistor:
[tex]\[
\text{Voltage drop} = 1.2 \, A \times 6 \, \Omega = 7.2 \, V
\][/tex]
So, the total resistance in the circuit is [tex]\(10 \Omega\)[/tex], the current flowing through the circuit is [tex]\(1.2 A\)[/tex], the voltage drop across the [tex]\(4 \Omega\)[/tex] resistor is [tex]\(4.8 V\)[/tex], and the voltage drop across the [tex]\(6 \Omega\)[/tex] resistor is [tex]\(7.2 V\)[/tex].
1. Total Resistance:
In a series circuit, the total resistance is simply the sum of all the resistances.
- We have two resistors: a [tex]\(4 \Omega\)[/tex] resistor and a [tex]\(6 \Omega\)[/tex] resistor.
- Total resistance [tex]\(R_{total} = 4 \Omega + 6 \Omega = 10 \Omega\)[/tex].
2. Current in the Circuit:
We can calculate the current in the circuit using Ohm's Law, which 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.
- The total voltage from the battery is [tex]\(12 V\)[/tex].
- Using the total resistance, the current [tex]\(I = \frac{12 \, V}{10 \, \Omega} = 1.2 \, A\)[/tex].
3. Voltage Drop Across Each Resistor:
The voltage drop across a resistor in a series circuit can be found using Ohm's Law, [tex]\(V = I \times R\)[/tex].
- For the [tex]\(4 \Omega\)[/tex] resistor:
[tex]\[
\text{Voltage drop} = 1.2 \, A \times 4 \, \Omega = 4.8 \, V
\][/tex]
- For the [tex]\(6 \Omega\)[/tex] resistor:
[tex]\[
\text{Voltage drop} = 1.2 \, A \times 6 \, \Omega = 7.2 \, V
\][/tex]
So, the total resistance in the circuit is [tex]\(10 \Omega\)[/tex], the current flowing through the circuit is [tex]\(1.2 A\)[/tex], the voltage drop across the [tex]\(4 \Omega\)[/tex] resistor is [tex]\(4.8 V\)[/tex], and the voltage drop across the [tex]\(6 \Omega\)[/tex] resistor is [tex]\(7.2 V\)[/tex].
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