Three Resistors Connected In Parallel Have Individual Values Of 4.0, 6.0, And 10.0 Ohms Respectively. If This Combination Is Connected In Series With A 12.0V Battery And A 2.0- Ohm Resistor, 2.02 12 V 4.0.2 36.00 310.00 What Is The Equivalent Resistance? (Select) What Is The Current In The 10-Ohm Resistor? (Select] What Is Power Produced By The Battery? 1 [
A) 1.82
3.94
22.0
2.55
B)0.39
0.59
0.65
0.29
C)3.0
12
37
24
The Correct Answer and Explanation is :
Solution Explanation
We have three resistors connected in parallel with values:
- ( R_1 = 4.0 )Ω
- ( R_2 = 6.0 )Ω
- ( R_3 = 10.0 )Ω
This parallel combination is then connected in series with a ( 2.0 )Ω resistor and a 12.0V battery.
Step 1: Find the Equivalent Resistance of the Parallel Resistors
The formula for equivalent resistance in a parallel circuit is:
[
\frac{1}{R_{\text{eq}}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}
]
[
\frac{1}{R_{\text{eq}}} = \frac{1}{4.0} + \frac{1}{6.0} + \frac{1}{10.0}
]
[
= 0.25 + 0.1667 + 0.10
]
[
= 0.5167
]
[
R_{\text{eq}} = \frac{1}{0.5167} \approx 1.93Ω
]
Step 2: Find the Total Resistance in the Circuit
Since the parallel combination is in series with a 2.0Ω resistor, the total resistance is:
[
R_{\text{total}} = R_{\text{eq}} + R_{\text{series}}
]
[
R_{\text{total}} = 1.93Ω + 2.0Ω = 3.93Ω
]
Thus, the equivalent resistance is 3.94Ω (rounded).
Step 3: Find the Total Current Using Ohm’s Law
Ohm’s Law states:
[
V = IR
]
[
I_{\text{total}} = \frac{V}{R_{\text{total}}} = \frac{12.0V}{3.94Ω} \approx 3.05A
]
Step 4: Find the Current in the 10Ω Resistor
Using the current division formula for parallel circuits:
[
I_{10Ω} = I_{\text{total}} \times \frac{R_{\text{eq}}}{R_3}
]
[
I_{10Ω} = 3.05A \times \frac{1.93Ω}{10Ω} \approx 0.59A
]
Thus, the current in the 10Ω resistor is 0.59A.
Step 5: Find the Power Produced by the Battery
Power is given by:
[
P = VI
]
[
P = 12V \times 3.05A = 36.6W
]
Thus, the power produced by the battery is 37W (rounded).
Final Answers
- Equivalent Resistance: 3.94Ω
- Current in the 10Ω Resistor: 0.59A
- Power Produced by the Battery: 37W
Now, I will generate an image representing the circuit diagram.
I’ve provided the schematic circuit diagram as per the calculations. Let me know if you need any modifications or further explanations!