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Numerical · Q22

Q.In the network shown, R1=4 ΩR_1 = 4\ \Omega and R2=4 ΩR_2 = 4\ \Omega are connected in parallel; this combination is joined in series with R3=3 ΩR_3 = 3\ \Omega; and the whole series combination is then connected in parallel with R4=5 ΩR_4 = 5\ \Omega. Find the equivalent resistance of the complete network.

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✓ Free question

Given R1=4 ΩR_1=4\ \Omega, R2=4 ΩR_2=4\ \Omega (parallel), then in series with R3=3 ΩR_3=3\ \Omega, the whole thing in parallel with R4=5 ΩR_4=5\ \Omega.

Step 1 (R1∥R2R_1\|R_2):

R12=R1R2R1+R2=4×44+4=168=2 ΩR_{12} = \frac{R_1R_2}{R_1+R_2} = \frac{4\times4}{4+4} = \frac{16}{8} = 2\ \Omega

Step 2 (series with R3R_3):

R123=R12+R3=2+3=5 ΩR_{123} = R_{12}+R_3 = 2+3 = 5\ \Omega

Step 3 (parallel with R4R_4):

Req=R123R4R123+R4=5×55+5=2510=2.5 ΩR_{\text{eq}} = \frac{R_{123}R_4}{R_{123}+R_4} = \frac{5\times5}{5+5} = \frac{25}{10} = 2.5\ \Omega

✓Final answer

The equivalent resistance of the complete network is 2.5 Ω2.5\ \Omega.

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