Both batteries in Figure are ideal. Emf E_1 of battery 1 has a fixed value, but

Question

Both batteries in Figure are ideal. Emf E_1 of battery 1 has a fixed value, but emf E_2 of battery 2 can be varied between 29.0 V and 290.0 V. The plots in Figure (b) give the currents through the two batteries as a function of E_2. The vertical scale is set by I_S = 0.78 A. You must decide which plot corresponds to which battery, but for both plots, a negative current occurs when the direction of the current through the battery is opposite the direction of that battery's emf. What are emf E_1, resistance R_1, and resistance R_2?

Explanation / Answer

dark line has to be of E2 as at high E2, current is positive in that.

When E2 = 116 V, current through E2 =0, current through E1 =0.39 A

so, E1 -0.39R1 = 116

0.39 R2 = 116

R2 = 116/0.39 = 297.4 ohm

when E2=174 V, current through R1=0

so E1= 174 V

R1 = (174-116)/0.39 = 148.7 ohm

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