Calculating Total Current for Parallel Resistors
The problem asks for the total current supplied by the voltage source when two \(100\text{-}\Omega\) resistors are connected in parallel across a \(40\text{-}\text{V}\) supply.
Step 1: Calculate Equivalent Resistance
When resistors are connected in parallel, the reciprocal of the equivalent resistance (\(R_{eq}\)) is the sum of the reciprocals of individual resistances. For two resistors, the formula simplifies to:
\( R_{eq} = \frac{R_1 \times R_2}{R_1 + R_2} \)
Given \(R_1 = 100\text{ }\Omega\) and \(R_2 = 100\text{ }\Omega\):
\( R_{eq} = \frac{100\text{ }\Omega \times 100\text{ }\Omega}{100\text{ }\Omega + 100\text{ }\Omega} = \frac{10000\text{ }\Omega^2}{200\text{ }\Omega} = 50\text{ }\Omega \)
Step 2: Apply Ohm's Law
Ohm's Law states that the voltage (\(V\)) across a circuit (or component) is equal to the product of the current (\(I\)) flowing through it and its resistance (\(R\)): \(V = I \times R\). To find the current supplied by the source, we rearrange the formula to \(I = \frac{V}{R}\).
Using the supply voltage (\(V = 40\text{ V}\)) and the calculated equivalent resistance (\(R_{eq} = 50\text{ }\Omega\)):
\( I = \frac{40\text{ V}}{50\text{ }\Omega} = \frac{4}{5}\text{ A} = 0.8\text{ A} \)
Therefore, the current supplied by the voltage source is \(0.8\text{ A}\).
Similar Questions
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Important Questions from Combination of Resistors — Series and Parallel
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Three resistor, each equal to 3 Ω are connected so as to form a triangle. The equivalent resistance between any two vertices of the triangle is:
- Two resistors R 1 and R 2 arranged in parallel combination in an electrical closed circuit are made of the same material and of the same thickness. If the length of R 2 is twice the length of R 1, then the total resistance R satisfies
