The circuit shown in the figure consists of ideal batteries ?1 =20V and ?2 =20V, resistors ? =600Ω, ?1 =600Ω and initially uncharged two capacitors with capacitances ?1 = ?2 =10mF. The circuit is completed when switch S is closed at time t=0. Use the loop rules and the relationship between the charging current i and the charge q of the capacitors a) to obtain a differential equation that allows you to determine how the charge q of the capacitors varies with time. b) What are the capacitor charges if the switch S is closed for a long time? c) Find the current through the battery ?1 at time t = 3 s after the switch closes.

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