Parallel resistor circuit powered by a 12V battery.
Circuit diagram showing a 12V battery connected in parallel with four resistors (R1, R2, R3, R4).
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Step-by-step solution for: Ohm& #39;s Law - AP Physics 1
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Show Answer Key & Explanations
Step-by-step solution for: Ohm& #39;s Law - AP Physics 1
To solve for the properties of this circuit, we need to understand how parallel circuits work. Since specific resistance values for R1, R2, R3, and R4 were not provided in the problem description, I will explain the general rules and formulas you need to use to find the answer based on whatever numbers your homework gives you.
In a parallel circuit (where components are connected side-by-side like rungs on a ladder), the voltage across each branch is the same as the source voltage.
* Source Voltage: 12V
* Voltage across R1: 12V
* Voltage across R2: 12V
* Voltage across R3: 12V
* Voltage across R4: 12V
Rule: $V_{total} = V_1 = V_2 = V_3 = V_4 = 12\text{V}$
Once you know the voltage across each resistor, you can find the current flowing through each one using Ohm's Law ($I = \frac{V}{R}$). You will need the specific ohm ($\Omega$) values for R1, R2, R3, and R4 from your assignment.
* Current through R1 ($I_1$) = $\frac{12}{R_1}$
* Current through R2 ($I_2$) = $\frac{12}{R_2}$
* Current through R3 ($I_3$) = $\frac{12}{R_3}$
* Current through R4 ($I_4$) = $\frac{12}{R_4}$
The total current leaving the battery is the sum of the currents flowing through all the individual branches.
* Formula: $I_{total} = I_1 + I_2 + I_3 + I_4$
If you need to find the total equivalent resistance ($R_{eq}$) of the whole circuit, you use the reciprocal formula for parallel resistors:
* Formula: $\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \frac{1}{R_4}$
Alternatively, if you already calculated the Total Current in Step 3, you can just use Ohm's Law for the whole circuit:
* $R_{eq} = \frac{V_{total}}{I_{total}} = \frac{12}{I_{total}}$
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Example Calculation:
Imagine your homework says:
$R_1 = 4\,\Omega$, $R_2 = 6\,\Omega$, $R_3 = 12\,\Omega$, $R_4 = 12\,\Omega$.
1. Currents:
* $I_1 = 12 / 4 = 3\,\text{A}$
* $I_2 = 12 / 6 = 2\,\text{A}$
* $I_3 = 12 / 12 = 1\,\text{A}$
* $I_4 = 12 / 12 = 1\,\text{A}$
2. Total Current:
* $I_{total} = 3 + 2 + 1 + 1 = 7\,\text{A}$
3. Total Resistance:
* $R_{eq} = 12\text{V} / 7\text{A} \approx 1.71\,\Omega$
Since I do not have your specific resistor values, I cannot give a single numerical final answer. Please apply the steps above using the numbers provided in your specific problem statement.
Final Answer:
Please provide the resistance values for R1, R2, R3, and R4 to get a specific numerical solution. Generally, the voltage across each resistor is 12V, and the total current is the sum of the individual currents ($I_{total} = \frac{12}{R_1} + \frac{12}{R_2} + \frac{12}{R_3} + \frac{12}{R_4}$).
Step 1: Understand Voltage in Parallel Circuits
In a parallel circuit (where components are connected side-by-side like rungs on a ladder), the voltage across each branch is the same as the source voltage.
* Source Voltage: 12V
* Voltage across R1: 12V
* Voltage across R2: 12V
* Voltage across R3: 12V
* Voltage across R4: 12V
Rule: $V_{total} = V_1 = V_2 = V_3 = V_4 = 12\text{V}$
Step 2: Calculate Current for Each Resistor
Once you know the voltage across each resistor, you can find the current flowing through each one using Ohm's Law ($I = \frac{V}{R}$). You will need the specific ohm ($\Omega$) values for R1, R2, R3, and R4 from your assignment.
* Current through R1 ($I_1$) = $\frac{12}{R_1}$
* Current through R2 ($I_2$) = $\frac{12}{R_2}$
* Current through R3 ($I_3$) = $\frac{12}{R_3}$
* Current through R4 ($I_4$) = $\frac{12}{R_4}$
Step 3: Calculate Total Current
The total current leaving the battery is the sum of the currents flowing through all the individual branches.
* Formula: $I_{total} = I_1 + I_2 + I_3 + I_4$
Step 4: Calculate Total Resistance (Optional)
If you need to find the total equivalent resistance ($R_{eq}$) of the whole circuit, you use the reciprocal formula for parallel resistors:
* Formula: $\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \frac{1}{R_4}$
Alternatively, if you already calculated the Total Current in Step 3, you can just use Ohm's Law for the whole circuit:
* $R_{eq} = \frac{V_{total}}{I_{total}} = \frac{12}{I_{total}}$
---
Example Calculation:
Imagine your homework says:
$R_1 = 4\,\Omega$, $R_2 = 6\,\Omega$, $R_3 = 12\,\Omega$, $R_4 = 12\,\Omega$.
1. Currents:
* $I_1 = 12 / 4 = 3\,\text{A}$
* $I_2 = 12 / 6 = 2\,\text{A}$
* $I_3 = 12 / 12 = 1\,\text{A}$
* $I_4 = 12 / 12 = 1\,\text{A}$
2. Total Current:
* $I_{total} = 3 + 2 + 1 + 1 = 7\,\text{A}$
3. Total Resistance:
* $R_{eq} = 12\text{V} / 7\text{A} \approx 1.71\,\Omega$
Since I do not have your specific resistor values, I cannot give a single numerical final answer. Please apply the steps above using the numbers provided in your specific problem statement.
Final Answer:
Please provide the resistance values for R1, R2, R3, and R4 to get a specific numerical solution. Generally, the voltage across each resistor is 12V, and the total current is the sum of the individual currents ($I_{total} = \frac{12}{R_1} + \frac{12}{R_2} + \frac{12}{R_3} + \frac{12}{R_4}$).
Parent Tip: Review the logic above to help your child master the concept of ohms law practice worksheet.
