1. In the figure the ideal batteries have emfs ? 1 = 10.0 V and ? 2 = 0.500 ? 1

Question

1. In the figure the ideal batteries have emfs ?1 = 10.0 V and ?2 = 0.500 ?1, and the resistances are each 3.61 ?. What is the value of current in (a) resistor 2 and (b) resistor 3?

2. The figure shows a circuit of four resistors that are connected to a larger circuit. The graph below the circuit shows the electric potential V(x) as a function of position x along the lower branch of the circuit, through resistor 4; the potential VA is 11.7 V. The graph above the circuit shows the electric potential V(x) versus position x along the upper branch of the circuit, through resistors 1, 2, and 3; the potential differences are ?VB = 2.23 V and ?VC = 4.74 V. Resistor 3 has a resistance of 200 ?. What is the resistance of (a) resistor 1 and (b) resistor 2?

Explanation / Answer

1)   u need to make 2 eqns with 2 unknowns :
KCL gives i3 = i1 + i2

KVL in the right loop will give :
5.0= R2 i2 + R3 (i1 + i2) => 5.0 = 7.22 i2 + 3.61 i1 ..... (1)

KVL in the left loop will give :
10 = 7.22 i1 + 3.61 i2 ... (2)
mult (2) by 2 and subtract (2) - (1) u get :
20 - 5.0 = (14.44 - 3.61) i1 + 0
=> i1 = 1.385 A
and i2 = 0 A
so i3 = i1 = 1.385 A

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