Given the following series circuit R, R, R, 100 2 300 2 50 Ω 9 V Calculate the current I of the circuit and the voltage on the resistors VR1, VR2 and VR3

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**Series Circuit Problem**

**Description:**
Given the following series circuit, calculate the current \( I \) of the circuit and the voltage across the resistors \( VR1 \), \( VR2 \), and \( VR3 \).

**Circuit Details:**
- A series circuit with a voltage source of 9 volts.
- Three resistors are connected in series:
  - \( R_1 = 100 \, \Omega \)
  - \( R_2 = 300 \, \Omega \)
  - \( R_3 = 50 \, \Omega \)

**Analysis:**
To solve the problem:
1. Calculate the total resistance \( R_{total} \) in the circuit:
   \[
   R_{total} = R_1 + R_2 + R_3 = 100 \, \Omega + 300 \, \Omega + 50 \, \Omega = 450 \, \Omega
   \]

2. Use Ohm’s law to find the current \( I \):
   \[
   I = \frac{V}{R_{total}} = \frac{9 \, V}{450 \, \Omega} = 0.02 \, A
   \]

3. Calculate the voltage across each resistor using \( V = IR \):
   - Voltage across \( R_1 \) (\( VR1 \)):
     \[
     VR1 = I \times R_1 = 0.02 \, A \times 100 \, \Omega = 2 \, V
     \]
   - Voltage across \( R_2 \) (\( VR2 \)):
     \[
     VR2 = I \times R_2 = 0.02 \, A \times 300 \, \Omega = 6 \, V
     \]
   - Voltage across \( R_3 \) (\( VR3 \)):
     \[
     VR3 = I \times R_3 = 0.02 \, A \times 50 \, \Omega = 1 \, V
     \]
Transcribed Image Text:**Series Circuit Problem** **Description:** Given the following series circuit, calculate the current \( I \) of the circuit and the voltage across the resistors \( VR1 \), \( VR2 \), and \( VR3 \). **Circuit Details:** - A series circuit with a voltage source of 9 volts. - Three resistors are connected in series: - \( R_1 = 100 \, \Omega \) - \( R_2 = 300 \, \Omega \) - \( R_3 = 50 \, \Omega \) **Analysis:** To solve the problem: 1. Calculate the total resistance \( R_{total} \) in the circuit: \[ R_{total} = R_1 + R_2 + R_3 = 100 \, \Omega + 300 \, \Omega + 50 \, \Omega = 450 \, \Omega \] 2. Use Ohm’s law to find the current \( I \): \[ I = \frac{V}{R_{total}} = \frac{9 \, V}{450 \, \Omega} = 0.02 \, A \] 3. Calculate the voltage across each resistor using \( V = IR \): - Voltage across \( R_1 \) (\( VR1 \)): \[ VR1 = I \times R_1 = 0.02 \, A \times 100 \, \Omega = 2 \, V \] - Voltage across \( R_2 \) (\( VR2 \)): \[ VR2 = I \times R_2 = 0.02 \, A \times 300 \, \Omega = 6 \, V \] - Voltage across \( R_3 \) (\( VR3 \)): \[ VR3 = I \times R_3 = 0.02 \, A \times 50 \, \Omega = 1 \, V \]
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