Calculate the effective Inet resistance of the ffg diagram.

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ScanSolve AI Tutor · Accepted Answer

Here are the calculations for the effective resistance of each diagram. a) Step 1: Calculate the equivalent resistance of the parallel combination of 3 Ω and 6 Ω. Rp1 = (R₁ R₂)/(R₁ + R₂) = (3 Ω × 6 Ω)/(3 Ω + 6 Ω) = (18 Ω²)/(9 Ω) = 2 Ω Step 2: Add this equivalent resistance to the series resistors (1 Ω and 4 Ω). Rtotal, a = 1 Ω + 4 Ω + Rp1 = 1 Ω + 4 Ω + 2 Ω = 7 Ω The effective resistance for diagram (a) is 7 Ω. b) Step 1: Calculate the equivalent resistance of the first parallel combination (2 Ω, 4 Ω, and 8 Ω). 1/Rp1 = (1)/(2 Ω) + (1)/(4 Ω) + (1)/(8 Ω); 1/Rp1 = (4)/(8 Ω) + (2)/(8 Ω) + (1)/(8 Ω) = (4+2+1)/(8 Ω) = (7)/(8 Ω); Rp1 = 8/7 Ω ≈ 1.143 Ω Step 2: Calculate the equivalent resistance of the second parallel combination (3 Ω and 5 Ω). Rp2 = (R₃ R₄)/(R₃ + R₄) = (3 Ω × 5 Ω)/(3 Ω + 5 Ω) = (15 Ω²)/(8 Ω) = 1.875 Ω Step 3: Add these equivalent resistances to the series resistor (10 Ω). Rtotal, b = Rp1 + Rp2 + 10 Ω = 8/7 Ω + 1.875 Ω + 10 Ω; Rtotal, b ≈ 1.143 Ω + 1.875 Ω + 10 Ω = 13.018 Ω The effective resistance for diagram (b) is approximately 13.018 Ω.

Calculate the effective Inet resistance of the ffg diagram.

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Step-by-step solution

Part a· 2 steps

Calculate the equivalent resistance of the parallel combination of $3 \, \Omega$ and $6 \, \Omega$ .

Add this equivalent resistance to the series resistors ( $1 \, \Omega$ and $4 \, \Omega$ ).

Part b· 3 steps
$\text{13.018 } \Omega$

Calculate the equivalent resistance of the first parallel combination ( $2 \, \Omega$ , $4 \, \Omega$ , and $8 \, \Omega$ ).

Calculate the equivalent resistance of the second parallel combination ( $3 \, \Omega$ and $5 \, \Omega$ ).

Add these equivalent resistances to the series resistor ( $10 \, \Omega$ ).

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Calculate the effective Inet resistance of the ffg diagram.

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Step-by-step solution

Part a· 2 steps

Calculate the equivalent resistance of the parallel combination of 3 Ω3 \, \Omega3Ω and 6 Ω6 \, \Omega6Ω.

Add this equivalent resistance to the series resistors (1 Ω1 \, \Omega1Ω and 4 Ω4 \, \Omega4Ω).

Part b· 3 steps13.018 Ω\text{13.018 } \Omega13.018 Ω

Calculate the equivalent resistance of the first parallel combination (2 Ω2 \, \Omega2Ω, 4 Ω4 \, \Omega4Ω, and 8 Ω8 \, \Omega8Ω).

Calculate the equivalent resistance of the second parallel combination (3 Ω3 \, \Omega3Ω and 5 Ω5 \, \Omega5Ω).

Add these equivalent resistances to the series resistor (10 Ω10 \, \Omega10Ω).

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Still stuck on this one?

More Physics Questions

Calculate the equivalent resistance of the parallel combination of $3 \, \Omega$ and $6 \, \Omega$ .

Add this equivalent resistance to the series resistors ( $1 \, \Omega$ and $4 \, \Omega$ ).

Part b· 3 steps
$\text{13.018 } \Omega$

Calculate the equivalent resistance of the first parallel combination ( $2 \, \Omega$ , $4 \, \Omega$ , and $8 \, \Omega$ ).

Calculate the equivalent resistance of the second parallel combination ( $3 \, \Omega$ and $5 \, \Omega$ ).

Add these equivalent resistances to the series resistor ( $10 \, \Omega$ ).