What is the voltage drop across the 100 Ohm resistor With an 8 V battery and with a 100 and 300 ohm resistor
The Correct Answer and Explanation is:
To determine the voltage drop across the 100-ohm resistor in a circuit with a battery and resistors, we need to consider the following details:
Circuit Details:
- The battery provides a total voltage of 8 V.
- There are two resistors: 100 ohms and 300 ohms.
Assumptions:
We assume the resistors are connected in series, as this is a typical setup for calculating voltage drops across individual resistors in a simple circuit.
Step-by-Step Calculation:
- Calculate the total resistance (R_total):
Since the resistors are in series, the total resistance is simply the sum of the individual resistances:
[
R_{\text{total}} = R_1 + R_2 = 100 \, \Omega + 300 \, \Omega = 400 \, \Omega
] - Calculate the total current (I):
Using Ohm’s Law, ( V = IR ), where ( V ) is the voltage, ( I ) is the current, and ( R ) is the total resistance. Rearranging for current:
[
I = \frac{V}{R_{\text{total}}} = \frac{8 \, \text{V}}{400 \, \Omega} = 0.02 \, \text{A}
]
So, the current flowing through the circuit is 0.02 A (20 mA). - Calculate the voltage drop across the 100-ohm resistor:
Again, using Ohm’s Law (( V = IR )), the voltage drop across the 100-ohm resistor is:
[
V_{\text{100Ω}} = I \times R_1 = 0.02 \, \text{A} \times 100 \, \Omega = 2 \, \text{V}
]
Thus, the voltage drop across the 100-ohm resistor is 2 V.
Explanation:
In a series circuit, the same current flows through all components. The voltage drop across each resistor depends on its resistance. Since the total resistance of the circuit is 400 ohms, and the current flowing is 0.02 A, the voltage drop across each resistor can be found using Ohm’s Law. The 100-ohm resistor will have a voltage drop of 2 V, while the 300-ohm resistor will have a larger voltage drop, as its resistance is greater. The total voltage from the battery is distributed across the resistors in proportion to their resistances. Therefore, the voltage across the 100-ohm resistor is 2 V, leaving 6 V across the 300-ohm resistor.