A 1.5 volts cell is connected to a 20 ohm resistor connected in series with a 40 ohm resistor. (a) What is the total current in the circuit? (B) What is the voltage drop across the 40 ohm resistor
The Correct Answer and Explanation is:
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Solution:
Given:
- Voltage of the cell (V) = 1.5 volts
- Resistors: R₁ = 20 ohms, R₂ = 40 ohms, connected in series
(a) Total current in the circuit
For resistors in series, the total resistance is given by:
Rₜ = R₁ + R₂ = 20 ohms + 40 ohms = 60 ohms
Using Ohm’s Law, the total current (I) is:
I = V / Rₜ = 1.5 volts / 60 ohms = 0.025 amperes or 25 milliamperes
(b) Voltage drop across the 40 ohm resistor
The same current flows through all components in a series circuit, so:
Voltage drop (V₂) = I × R₂ = 0.025 A × 40 ohms = 1.0 volt
Explanation
In this problem, we are dealing with a simple electrical circuit that consists of a 1.5 volt battery connected in series with two resistors of 20 ohms and 40 ohms. When resistors are connected in series, their resistances add up directly. This means the total resistance of the circuit is the sum of the two resistors, which is 60 ohms.
Once the total resistance is known, we can apply Ohm’s Law to calculate the total current flowing in the circuit. Ohm’s Law states that the current is equal to the total voltage divided by the total resistance. Here, the battery provides 1.5 volts and the total resistance is 60 ohms. When we perform the division, we get a current of 0.025 amperes, which is the same as 25 milliamperes.
In a series circuit, the same current passes through all components, meaning both resistors have the same current of 0.025 amperes flowing through them. The voltage drop across each resistor can be found individually by multiplying the current by the resistance of that resistor.
For the 40 ohm resistor, the voltage drop is calculated as 0.025 amperes times 40 ohms, giving a value of 1.0 volt. This means out of the 1.5 volts supplied by the battery, 1.0 volt is used across the 40 ohm resistor, and the remaining 0.5 volts is dropped across the 20 ohm resistor. The sum of voltage drops equals the total battery voltage, which confirms the calculations are correct.
