Question
Create a series circuit with a 20-volt battery and four 20-ohm resistors, as shown. Measure the current.
Based on the voltage and current, what is the resistance of the circuit?
(Hint: Use Ohm’s law.)
0.25A
Ohmmeters measure resistance. Remove the battery and attach the terminals of the Ohmmeter () to the ends of the circuit, where the battery used to be attached.
What is the resistance?
33.0A
Make a rule: How do you calculate the total resistance of a series circuit?
Based on the voltage and current, what is the resistance of the circuit?
(Hint: Use Ohm’s law.)
0.25A
Ohmmeters measure resistance. Remove the battery and attach the terminals of the Ohmmeter () to the ends of the circuit, where the battery used to be attached.
What is the resistance?
33.0A
Make a rule: How do you calculate the total resistance of a series circuit?
Answers
GPT-4o mini
To calculate the total resistance in a series circuit, you simply add the resistance values of all the components together. The formula for calculating the total resistance (\( R_{\text{total}} \)) in a series circuit is:
\[
R_{\text{total}} = R_1 + R_2 + R_3 + R_4 + \ldots + R_n
\]
In your case, with four 20-ohm resistors in series:
\[
R_{\text{total}} = 20 \, \Omega + 20 \, \Omega + 20 \, \Omega + 20 \, \Omega = 80 \, \Omega
\]
**Using Ohm's Law:**
Ohm’s Law states that \( V = I \cdot R \), where:
- \( V \) is the voltage (in volts),
- \( I \) is the current (in amperes),
- \( R \) is the resistance (in ohms).
Given the total voltage of 20 volts and a measured current of 0.25 A, we can check the resistance using Ohm's law:
\[
R = \frac{V}{I} = \frac{20 \, V}{0.25 \, A} = 80 \, \Omega
\]
This matches the calculated total resistance based on the resistors.
**Using an Ohmmeter:**
When you attach an ohmmeter across the circuit previously containing the battery, it should also measure the resistance in the same way, showing the total resistance of the series circuit. It appears that you may have provided a current reading of 33.0 A, which seems incorrect as it should provide a resistance reading instead.
When the ohmmeter is used, it should indicate:
\[
R_{\text{total}} = 80 \, \Omega
\]
**Rule Recap:**
1. **To calculate total resistance in a series circuit, add the resistances together:**
\[
R_{\text{total}} = R_1 + R_2 + R_3 + \ldots
\]
2. **Use Ohm's Law to confirm resistance as needed:**
\[
R = \frac{V}{I}
\]
This will ensure you account for all resistances in any series circuit configurations.
\[
R_{\text{total}} = R_1 + R_2 + R_3 + R_4 + \ldots + R_n
\]
In your case, with four 20-ohm resistors in series:
\[
R_{\text{total}} = 20 \, \Omega + 20 \, \Omega + 20 \, \Omega + 20 \, \Omega = 80 \, \Omega
\]
**Using Ohm's Law:**
Ohm’s Law states that \( V = I \cdot R \), where:
- \( V \) is the voltage (in volts),
- \( I \) is the current (in amperes),
- \( R \) is the resistance (in ohms).
Given the total voltage of 20 volts and a measured current of 0.25 A, we can check the resistance using Ohm's law:
\[
R = \frac{V}{I} = \frac{20 \, V}{0.25 \, A} = 80 \, \Omega
\]
This matches the calculated total resistance based on the resistors.
**Using an Ohmmeter:**
When you attach an ohmmeter across the circuit previously containing the battery, it should also measure the resistance in the same way, showing the total resistance of the series circuit. It appears that you may have provided a current reading of 33.0 A, which seems incorrect as it should provide a resistance reading instead.
When the ohmmeter is used, it should indicate:
\[
R_{\text{total}} = 80 \, \Omega
\]
**Rule Recap:**
1. **To calculate total resistance in a series circuit, add the resistances together:**
\[
R_{\text{total}} = R_1 + R_2 + R_3 + \ldots
\]
2. **Use Ohm's Law to confirm resistance as needed:**
\[
R = \frac{V}{I}
\]
This will ensure you account for all resistances in any series circuit configurations.