Four resistors are connected to a battery as shown in the figure. The current through the battery is I, the battery's electromotive force (emf) is E = 5.75 V, and the resistor values are R₁ = R, R₂ = 2R, R3 = 4R, and R4 = 3R. Find the voltages across each resistor. V₁ = V₂ = V3 = V4 = V V V V R₁ = R www R₂ = 2R R₁ = 3R ww R₂ = 4R

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Four resistors are connected to a battery as shown in the
figure. The current through the battery is I, the battery's
electromotive force (emf) is & = 5.75 V, and the resistor
values are R₁ = R, R₂ = 2R, R3 = 4R, and R₁ = 3R. Find
the voltages across each resistor.
V₁ =
V/₂ =
V3 =
V4 =
V
V
V
V
R₁ = R
www
R₂ = = 2R
www
R₁=3R
ww
R₂ = 4R
Transcribed Image Text:Four resistors are connected to a battery as shown in the figure. The current through the battery is I, the battery's electromotive force (emf) is & = 5.75 V, and the resistor values are R₁ = R, R₂ = 2R, R3 = 4R, and R₁ = 3R. Find the voltages across each resistor. V₁ = V/₂ = V3 = V4 = V V V V R₁ = R www R₂ = = 2R www R₁=3R ww R₂ = 4R
Expert Solution
Step 1: Calculation of the equivalent resistance of the circuit

From the given diagram we can say that R subscript 2 and R subscript 3 are in series, by adding them we get equivalent resistance in series is

R subscript s equals R subscript 2 plus R subscript 3
R subscript s equals 2 R plus 4 R
R subscript s equals 6 R

Now this R subscript s is in parallel with resistance R subscript 4, then equivalent resistance in parallel is

 1 over R subscript p equals 1 over R subscript s plus 1 over R subscript 4
rightwards double arrow 1 over R subscript p equals fraction numerator 1 over denominator 6 R end fraction plus fraction numerator 1 over denominator 3 R end fraction
rightwards double arrow R subscript p equals fraction numerator 3 R cross times 6 R over denominator 3 R plus 6 R end fraction
rightwards double arrow R subscript p equals 2 R

Now this R subscript p is in series with the resistance R subscript 1 then equivalent resistance for the circuit is,

R subscript e q end subscript equals R subscript p plus R subscript 1
R subscript e q end subscript equals 2 R plus R
R subscript e q end subscript equals 3 R

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