What does $R_{eq}$ equal? What does $R_T$ equal?
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Consider the network of four resistors shown in the diagram, where R1 = 2.00 ̩, R2 = 5.00 ̩, R3 = 1.00 ̩, and R4 = 7.00 ̩. The resistors are connected to a constant voltage of magnitude V. A. Find the equivalent resistance RA. of the resistor network. Express your answer in ohms.
Nishant K.
(a) The currents are as shown. From Ohm's law applied between 1 and 7 via 1487 (say) (b) Between 1 and 2 from the loop 14321 , $I_{1} R=2 I_{2} R+I_{3} R$ or, $I_{1}=I_{3}+2 I_{2}$ From the loop 48734 , $\left(I_{2}-I_{3}\right) R+2\left(I_{2}-I_{3}\right) R+\left(I_{2}-I_{3}\right) R=I_{3} R$ or, $4\left(I_{2}-I_{3}\right)=I_{3}$ or $I_{3}=\frac{4}{5} I_{2}$ so $I_{1}=\frac{14}{5} I_{2}$ Then, $\left(I_{1}+2 I_{2}\right) R_{e q}=\frac{24}{5} I_{2} R_{\mathrm{eq}}=I_{1} R=\frac{14}{5} I_{2} R$ or $R_{e q}=\frac{7}{12} R$ (c) Between 1 and 3 From the loop 15621 $$ \begin{aligned} &\qquad I_{2} R=I_{1} R+\frac{I_{1}}{2} R \text { or, } I_{2}=3 \frac{I_{1}}{2} \\ &\text { Then, } \begin{array}{c} \left(I_{1}+2 I_{2}\right) R_{e q}=4 I_{1} R_{e q} \\ & =I_{2} R+I_{2} R=3 I_{1} R \\ \text { Hence, } \quad R_{e q}=\frac{3}{4} R \end{array} \end{aligned} $$
Electrodynamics
Electric Current
Consider the network of four resistors shown in the diagram, where R1 = 2.00 Ω, R2 = 5.00 Ω, R3 = 1.00 Ω, and R4 = 7.00 Ω. The resistors are connected to a constant voltage of magnitude V. Part A Find the equivalent resistance RA of the resistor network. Express your answer in ohms. Part B Two resistors of resistance R5 = 3.00 Ω and R6 = 3.00 Ω are added to the network, and an additional resistor of resistance R7 = 3.00 Ω is connected by a switch, as shown in the diagram (Figure 2). Find the equivalent resistance RB of the new resistor network when the switch is open. Express your answer in ohms. Part C Find the equivalent resistance RC of the resistor network described in Part B when the switch is closed. Express your answer in ohms.
Shaiju T.
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