Problem Analysis
The problem asks for the voltage across each resistor in a parallel circuit. We are given:
- Two resistors, each with a resistance of \(20\ \Omega\).
- These resistors are connected in parallel.
- The parallel combination is connected across a voltage supply of \(40\ V\).
We need to find the voltage across each individual \(20\ \Omega\) resistor.
Parallel Circuit Voltage Property
A fundamental property of parallel circuits is that the voltage across all components connected in parallel is the same. This voltage is equal to the voltage of the source supplying the circuit.
In this specific circuit:
- The two \(20\ \Omega\) resistors are connected in parallel with each other.
- This parallel arrangement is directly connected to the \(40\ V\) supply.
Therefore, the voltage across the first resistor (\(V_1\)) must be equal to the supply voltage, and the voltage across the second resistor (\(V_2\)) must also be equal to the supply voltage.
Voltage Across Each Resistor
Applying the parallel circuit property:
- Voltage across the first resistor, \(V_1 = V_{supply}\)
- Voltage across the second resistor, \(V_2 = V_{supply}\)
Given that the supply voltage is \(40\ V\):
- \(V_1 = 40\ V\)
- \(V_2 = 40\ V\)
Thus, the voltage across each resistor is \(40\ V\).
Important Questions from Combination of Resistors — Series and Parallel
Consider two resistors, $R_1$ and $R_2$, connected in series to a DC voltage source. Which of the following statements accurately describes the distribution of current and voltage across these resistors?
A cell of negligible resistance and e.m.f 2 volt is connected to series combination of 2 ohm, 3 ohm and 5 ohm. The potential difference across the 3 ohm resistance is:
Two bulbs A, of (100w, 100v), and B of (60 w, 100v) are connected in series and across the series combination 200 v is applied. Which bulb will be fused?
3 resistors of 3 ohm each connected in series. What is the mean values of resistors?
The equivalent resistance of the resistances (two) joined in parallel is 6/5 Ω. When one of the resistance wire is broken, the effective resistance becomes 2Ω. The resistance of the wire that got broken was :
