Suppose voltage V is applied across a resistance R. The power dissipated in the resistance is P. Now the same voltage V is applied across a parallel combination of three equal resistors each of resistance R. Then the power dissipated in the second case wi

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Q: 9 (CDS-I/2017)
Suppose voltage V is applied across a resistance R. The power dissipated in the resistance is P. Now the same voltage V is applied across a parallel combination of three equal resistors each of resistance R. Then the power dissipated in the second case will be

question_subject: 

Science

question_exam: 

CDS-I

stats: 

0,15,16,2,18,11,0

keywords: 

{'equal resistors': [0, 0, 0, 2], 'resistance': [0, 0, 1, 2], 'parallel combination': [0, 0, 0, 3], 'power': [24, 3, 21, 61]}

In the given question, we are comparing two scenarios with the same voltage (V) applied across different arrangements of resistors.

In the first scenario, we have a single resistor of resistance R. The power dissipated in the resistor is denoted as P.

Power can be calculated using the formula P = V^2 / R. Therefore, in this case, P = V^2 / R.

In the second scenario, we have a parallel combination of three equal resistors, each with resistance R.

When resistors are connected in parallel, the equivalent resistance (Rp) is given by the formula 1/Rp = 1/R1 + 1/R2 + 1/R3. Since all three resistors have the same resistance (R), we can rewrite the equation as 1/Rp = 1/R + 1/R + 1/R, which simplifies to 1/Rp = 3/R. Solving for Rp, we get Rp = R/3.

Using the formula for power, P = V^2 / R, we can calculate the power dissipated in the second scenario. Substituting the value of Rp (R/3) in the formula, we get P = V^2 / (