IIT-JEE 2008 · Paper 1 · Physics Q25

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PhysicsSingle correct+3 / -1Question 25 of 69

Figure shows three resistor configurations R1, R2 and R3 connected to 3 V battery. If the power dissipated by the configuration R1, R2 and R3 is P1, P2 and P3, respectively, then

Three networks of 1 Ω resistors, each across a 3 V battery. R1: a vertical chain of three 1 Ω resistors from the top node T through nodes N1 and N2 to the bottom node; a fourth 1 Ω joins T to N2 (on the right) and a fifth joins N1 to the bottom node (on the left), so it is a balanced bridge with N1-N2 as the bridge arm. R2: a diamond of four 1 Ω resistors between a top and a bottom node, with a fifth 1 Ω directly from top to bottom; the battery is across top and bottom. R3: a diamond of four 1 Ω resistors (two parallel paths of 2 Ω) in series with a further 1 Ω, across the battery.

P1 > P2 > P3

P1 > P3 > P2

P2 > P1 > P3

P3 > P2 > P1

Answer and worked solution

Official answer: C

R1 is a balanced bridge: T-N1, N1-bottom, T-N2 and N2-bottom are all 1 Ω, so the N1-N2 resistor carries no current. Two parallel paths of 2 Ω: $R_1=1\ \Omega$ .

R2. The diamond (two parallel 2 Ω paths, i.e. 1 Ω) is in parallel with the direct 1 Ω: $R_2=0.5\ \Omega$ .

R3. The diamond (1 Ω) in series with 1 Ω: $R_3=2\ \Omega$ .

Power $P=V^2/R$ : $P_1=9$ W, $P_2=18$ W, $P_3=4.5$ W, so $P_2>P_1>P_3$ .

(C)

Topics:Series and parallel resistors Wheatstone bridge and metre bridge Electrical power and heating

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IIT-JEE 2008 · Paper 1, Physics question 25