Two resistors R1 and R2 are connected in parallel. The equivalent resistance is given by:

March 20, 2026Physics

ScanSolve AI Answer

March 20, 2026

Answer

(a)

Step 1: Resistors $R_1$ and $R_2$ are connected in parallel, so the voltage $V$ across both is the same.

Current through $R_1$ : $I_1 = \frac{V}{R_1}$

Current through $R_2$ : $I_2 = \frac{V}{R_2}$

I_1 = \frac{V}{R_1}

I_2 = \frac{V}{R_2}

Step 2: Total current $I = I_1 + I_2$

I = \frac{V}{R_1} + \frac{V}{R_2} = V \left( \frac{1}{R_1} + \frac{1}{R_2} \right)

Step 3: For equivalent resistance $R_{eq}$ , $I = \frac{V}{R_{eq}}$

\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2}

Step 4: Common denominator $R_1 R_2$

\frac{1}{R_{eq}} = \frac{R_2}{R_1 R_2} + \frac{R_1}{R_1 R_2} = \frac{R_1 + R_2}{R_1 R_2}

Step 5: Take reciprocal

R_{eq} = \frac{R_1 R_2}{R_1 + R_2}

This matches option (a).

(a)

Was this helpful?

Need help with your own homework?

Get instant step-by-step solutions to any question. Free to start.

Ask Your Question

Got a syllabus? Photograph it and I'll tell you what's due and what's worth the most.

More Physics Questions

QJe ne comprends pas le cour de cinématique QState TWO effects that a force can have on an object. Study illustrations A-E below. Identify the ty…QLe vecteur position d'un point mobile dans l'espace, muni d'un repère (O,i,j,k) est donné par OM = (…Qtotal charge QHow to reduce wasted energy

See all Physics questions →

Still have questions?

Quick Answer

Resistors R_1 and R_2 are connected in parallel, so the voltage V across both is the same.

Asked on March 20, 2026Physics

This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.

ScanSolve AI AnswerAnswered on March 20, 2026

Step 1: Resistors R_1 and R_2 are connected in parallel, so the voltage V across both is the same. Current through R_1: I_1 = (V)/(R_1) Current through R_2: I_2 = (V)/(R_2) I_1 = (V)/(R_1) I_2 = (V)/(R_2) Step 2: Total current I = I_1 + I_2 I = (V)/(R_1) + (V)/(R_2) = V ( (1)/(R_1) + (1)/(R_2) ) Step 3: For equivalent resistance R_eq, I = (V)/(R_eq) (1)/(R_eq) = (1)/(R_1) + (1)/(R_2) Step 4: Common denominator R_1 R_2 (1)/(R_eq) = (R_2)/(R_1 R_2) + (R_1)/(R_1 R_2) = (R_1 + R_2)/(R_1 R_2) Step 5: Take reciprocal R_eq = (R_1 R_2)/(R_1 + R_2) This matches option (a). (a)