Answer :
Sure! Let's go through the solution to this problem step-by-step:
1. Identify the Given Values:
- Battery Voltage (V) = 12 volts
- First Resistor (R1) = 4 ohms
- Second Resistor (R2) = 6 ohms
2. Find the Total Resistance:
- Since the resistors are in series, the total resistance (R_total) is the sum of the individual resistances.
- [tex]\( R_{\text{total}} = R_1 + R_2 = 4\, \Omega + 6\, \Omega = 10\, \Omega \)[/tex]
3. Calculate the Current in the Circuit:
- Use Ohm's Law, which states that current (I) is the total voltage (V) divided by the total resistance (R_total).
- [tex]\( I = \frac{V}{R_{\text{total}}} = \frac{12\, \text{V}}{10\, \Omega} = 1.2\, \text{A} \)[/tex]
4. Calculate the Voltage Drop Across Each Resistor:
- Using Ohm's Law, the voltage drop (V_drop) across a resistor can be found by multiplying the current (I) by the resistance (R) of that resistor.
- Voltage drop across the 4 ohm resistor:
- [tex]\( V_{\text{drop, R1}} = I \times R_1 = 1.2\, \text{A} \times 4\, \Omega = 4.8\, \text{V} \)[/tex]
- Voltage drop across the 6 ohm resistor:
- [tex]\( V_{\text{drop, R2}} = I \times R_2 = 1.2\, \text{A} \times 6\, \Omega = 7.2\, \text{V} \)[/tex]
Summarized, here's what we found:
- The total resistance in the circuit is 10 ohms.
- The current flowing through the circuit is 1.2 amperes.
- The voltage drop across the 4 ohm resistor is 4.8 volts.
- The voltage drop across the 6 ohm resistor is 7.2 volts.
These calculations help us understand how the voltage is distributed across each component in a series circuit!
1. Identify the Given Values:
- Battery Voltage (V) = 12 volts
- First Resistor (R1) = 4 ohms
- Second Resistor (R2) = 6 ohms
2. Find the Total Resistance:
- Since the resistors are in series, the total resistance (R_total) is the sum of the individual resistances.
- [tex]\( R_{\text{total}} = R_1 + R_2 = 4\, \Omega + 6\, \Omega = 10\, \Omega \)[/tex]
3. Calculate the Current in the Circuit:
- Use Ohm's Law, which states that current (I) is the total voltage (V) divided by the total resistance (R_total).
- [tex]\( I = \frac{V}{R_{\text{total}}} = \frac{12\, \text{V}}{10\, \Omega} = 1.2\, \text{A} \)[/tex]
4. Calculate the Voltage Drop Across Each Resistor:
- Using Ohm's Law, the voltage drop (V_drop) across a resistor can be found by multiplying the current (I) by the resistance (R) of that resistor.
- Voltage drop across the 4 ohm resistor:
- [tex]\( V_{\text{drop, R1}} = I \times R_1 = 1.2\, \text{A} \times 4\, \Omega = 4.8\, \text{V} \)[/tex]
- Voltage drop across the 6 ohm resistor:
- [tex]\( V_{\text{drop, R2}} = I \times R_2 = 1.2\, \text{A} \times 6\, \Omega = 7.2\, \text{V} \)[/tex]
Summarized, here's what we found:
- The total resistance in the circuit is 10 ohms.
- The current flowing through the circuit is 1.2 amperes.
- The voltage drop across the 4 ohm resistor is 4.8 volts.
- The voltage drop across the 6 ohm resistor is 7.2 volts.
These calculations help us understand how the voltage is distributed across each component in a series circuit!
